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June 29, 2016

Search: Find the lowest common denominator of 3/4 and 5/8

Number of results: 78,623

precal help
The numerator of a fraction is four less than the denominator The sum of the fraction and its reciprocal is 5/2 Find the numerator and denominator if each is a positive integer
September 21, 2012 by Anonymous

algerbra 2
B. The rational expression is not defined for any values of 20^2-180/4x^2+36+ 72 for which the denominator equals zero. Find the value(s) of for which the denominator equals zero.
October 23, 2013 by hannah

le
a fraction is such that the numerator is seven less than the square of the denominator. if six is added to the numerator and on to the denominator the result is 2. Find the fraction
August 21, 2015 by john

Maths
Find the denominator n of the rational number kn (k,n are both integers) such that ∣Root 2 - k/n∣ is the smallest possible, out of all rational numbers with denominator less than 1000?
May 29, 2013 by ABCD

maths
the denominator of a fraction is two more than the numerator.when we decrease the numerator by1 and increase the denominator by 3,we get 1/4.find the fraction
November 8, 2014 by anuj

KUAI HELP!
4/75, 2r/25, r/125 -1/x, 2/xy, x/y 1/a, 1/b write fractions as equivalent fractions with the least common denominator
November 6, 2013 by rian

math
how to use a common denominator to write an equivalent fraction for each fraction?
March 13, 2014 by sam

LCD
I need a reveiw on how to use the LCD least common denominator to add and subtract
March 23, 2008 by ALi

5th grade math
rewrite each pair of fractions as equivalent fractions with a common denominator? 2/3, 3/4
January 9, 2012 by Alexia

Algebra
2 divided by 5w+ 10, minus 3 divided by2w-4 2/(5w +10) - 3/(2w-4) ? That can be rewritten with a common denominator. (2/5)/(w+2) - (3/2)/(w-2) = [(2/5)(w-2) - (3/2)(w+2)]/(w^2-1) = [(-11/10)w - (19/5)]/(w^2-1) But it doesn't look any simpler that way.
April 20, 2007 by Tony

Physics
Problem 3- A 40 kg child swings in a swing supported by two ropes, each 3 m long. (a) If the tension in each rope at the lowest point is 350 N, a. find the child's speed at the lowest point. b. the force exerted by the seat on the child at the lowest point. (Neglect the mass ...
November 23, 2013 by Mariam

Math
How do you subract the fraction 2/5 and 4/9? Form a common denominator and subtract the numerators, like this: 20/45 - 18/45 = (20-18)/45 = ? I assume you wanted 2/5 subtracted from 4/9, not the other way around. If you want 2/5 - 4/9, the sign changes.
December 25, 2006 by Sanjana

Maths
The numerator of a is 5 less than the denominator. If 1 is added to both the numerator and the denominator the fraction would be 2/3. Find the fraction
June 21, 2014 by Naziba

maths
how do i solve this equation? 2/(x+1)=1/(x-1) - (1/(2x-1)) thx Get a common denominator (x+1)(x-1)(2x-1) then, each term, multipy it out. Gather terms, solve.
July 12, 2007 by Emma

Math 111 (College Algebra)
Rational number or irrational? And why? I have been challenged in my college algebra class to determine whether or not .12122122212222122221222221... (continuing forever)is a rational number or not. I need to prove one way or the other. I am lost! :-( I know that rational ...
September 8, 2009 by Eleonora

algebra
w10y12z _______ w6z5 Are those exponents like [(w^10)*(y^12)*z]/[(w^6)*(z^5)]? If so then you should have some rules telling you how to simplify ratios of expressions. If the exponent of the numerator's term is greater than the term's exponent in the denominator, then subtract...
September 18, 2006 by amanda

math help
How do you figure out a related sentence for fractions? (here is the problem) t + 1/8= 3/5 multipy the 1/8 by 5/5 or it is 5/40 Then, mulipy the 3/5 by 8/8 to 24/40 Finally subtract 5/40 from both sides. Think out why it is done this way. What do you mean by a "related ...
February 13, 2007 by Emily

rs aggarwal math class 8 chapter 8 soluation
in a fraction twince the numerator is 2 more than the denominator . if 3 is added to the numerator and to the denominator , the new fraction is 2/3 . find the original fraction.
April 13, 2016 by rs aggarwal class 8 math si

math
paul spends 2/3 of an hour exercising and 1/2 hour practicing the piano each day what is the least common denominator of these fractions?.
September 17, 2012 by jammy

math
the numerical expression for 7/8-3/4(2-1/6)-2/3 is equal to I made a common denominator of 24 21/24-1&+12/24+3/24-16/24 -15/24+3/24-16/24 -12/24-16/24 -28/24 both are divible by 2 -14/12 & divide both by 2 again to get -7/6 Is this correct? Thank you
January 2, 2013 by es

maths
the numerator and denominator of a fraction are in the ratio 3:2 if 3 is added to the numerator and 2 is subtracted from the denominator a new fraction is formed whose value is 9/4 find the original fraction?
August 23, 2015 by vinit

Math
The numerator of a fraction is two less than its denominator. When both numerator and denominator are increased by 3, the fraction is incre ased by 3/20. Find the original fraction. Pls include solution and workings thx :)
October 24, 2011 by Ghiffari

math
what is the greater common factor of 6/12 need all divisible numbers for both and put in lowest form as a fraction
March 9, 2011 by Kylie

Math
This is a fill in the blanks. The lowest common multiple is the ________ number the given numbers divide into evenly
February 16, 2014 by Anonymous

Math
Add or subtract the following rational expressions. Be sure to look for factors before trying to determine a common denominator, and simplify your answers, if possible. 16x-12/4x^2+5x-6-3/x+2
February 8, 2016 by Anonymous

Math help plz ASAP.
Rationalize each denominator. 6 + square root of 2 ____________________________ square root of 3 PLZ HELP..dont kno how to do this question.plz explain..thanks You have (6 + sqrt(2))/sqrt(3) multiply that by sqrt(3)/sqrt(3) to get [(6 + sqrt(2))*sqrt(3)]/3 and simplify To ...
October 15, 2006 by Karla

maths
These questions concern the integers 84, 126, 168 and 294. 1)Choose the option that is the lowest common multiple of the four integers. 2)Choose the option that is the highest common factor of the four integers. Options for them: A) 28 B) 42 C) 63 D) 294 E) 3528 F) 7056 G 10) ...
September 11, 2007 by z

Math - Maxima and Minima
The height, h, in metres, of a ski ramp over a horizonatal distance, x, in metres, is given by h(x)=0.01x^3-0.3x^2+60 for the interval 0 less than or equal to x less than or equal to 22. a) Find the vertical drop from the top of the ramp to the lowest point on the ramp. b) ...
October 23, 2010 by Anonymous

algebra
The denominator of a fraction is 12 more than the numerator. If 16 is added to the numerator and 16 is subtracted from the denominator, the value of the resulting fraction is equal to 2/1. Find the original fraction
August 10, 2009 by Sarah

algebra
The numerator of a fraction is 7 less than the denominator if three is added to the numerator and 9 is subtracted from the denominator the new fraction is equal to 3/2. Find the original fraction.
September 27, 2012 by steph

Math
The denominator of a fraction is one more then the numerator. If 2 were added to both the numerator and denominator, the new fraction equals 4/5. Find the original fraction.
December 18, 2014 by Charles

math
the difference between the numerator and denominator of a fraction is 5. if 5 is added to its denominator then the fraction is decreased by one of its one fourth 1(1/4). find the value of fraction
January 6, 2016 by sarath

math 116
Is it always necessary to have a common denominator to add and subtract fractions? Why? What about multiplication and division with fractions?
March 24, 2008 by Rosetta

Algebra 1
Solve the equation by multiplying each side by the least common denominator. 2/h-2 + 4/h+1 = 0 I know the answer is 5, but I do not know how to solve the problem. Please explain further.
April 18, 2008 by Nicole

math
Find the least common denominator for fractions with the given denominators of 6, 8 and 10. Explain also what the LCM for these numbers would be. (c).The average person drinks about 3 1/5 cups of coffee per day. If a person works 5 days a week for 50 weeks a year. Find how ...
January 10, 2009 by rosland

Mathematics
Find a fraction which reduces to 3/4 when the numerator and denominator are each decreased by 1, and which reduces to 4/5 when the numerator and denominator are each increased by 1.
January 17, 2012 by David

Mathematics
Find a fraction which reduces to 3/4 when the numerator and denominator are each decreased by 1, and which reduces to 4/5 when the numerator and denominator are each increased by 1.
January 17, 2012 by David

Maths
The first term of an AP is 12 and that of a GP is 6. The common difference and the common ratio are equal, so as are the sum of the fist 3 terms. Find the possible values of the common difference?
December 1, 2014 by Andre

Calculus II
So I'm trying to integrate a function using partial fractions. Here is the integral of interest: ∫(3x^2+5x+3)/[(x+2)(x^2+1)]dx. Since the numerator's degree of the polynomial is lesser than that of the denominator's degree, it is clear to separate. However, once I ...
April 25, 2016 by Justin

Algebra
The numerator of a fraction exceeds the denominator. If 3 is added to the numerator and 9 is subtracted from the denominator, the new fraction is equal to 5/2. Find the original fraction.
August 11, 2011 by Brandon

physics
The length of the auditory canal in humans averages about 2.5 cm. What is the second lowest standing wave frequency for a pipe of this length open at one end? Use 345 m/s for the speed of sound. I know that 4L=lambda, so lambda= 10cm. I know that f=v/lambda, so f=3450 Hz. But ...
March 3, 2011 by Trace

math
Find a fraction that reduces to 3/4 when both the numerator and denominator are decreased by i, and reduces to 4/5 when both the numerator and denominator are each increased by 1. I know the answer is 7/9, but i dont know how to solve (i must use a system of equations).
January 23, 2013 by Molly

Math
3 2 ----- - ------ 2a -2 1 - a 5 3 ----- - ------ 2x - 4 2 - x need a little understanding on these anyone? I dont understand the second term. Is it this? 3 2 ----- - ------ = 2a -2 1 - a 3 2 ----- - ------ = 2(a -1) 1 - a 3 2 ----- - ------ = 2(a -1) -( a-1) 3 2 3/2 +2...
August 7, 2005 by leleirvin

math
if there are 30 students in a class and 39 candys in a pack how many packs of candy do you have to buy so that there will be no left overs (hint us lowest common mutilple
September 20, 2009 by christina

Limits-Rationalizing
lim x->1 (1-(1/x^3))/ (1-(1/x^2)) I keep seeming to get a denominator of zero when I rationalized the denominator.
March 13, 2013 by Marcus

math,algebra
how do you solve this problem 3 and 1/3 subtracted by 1 and 2/3? Change the mixed number back to fractions with a common denominator. That would give you 5/3 subtracted from 10/3. How many thirds are left?
December 16, 2006 by jasmine20

algebra
simplify. assume no denominator is eual to zero. -10m-1y0r(numerator) -14m-7y-3r-4(denominator)
January 21, 2010 by trista

algebra help!!!!
Add: b^−3 ca^−1 −xc^−2 how would i do this ? Let me make sure I have the question right. We have b^(−3) ca(^−1) −xc^(−2 )=? You might also write this as (1/b^3) c(1/a) − x(1/c)= c/(a*b^3) - x/c=? If this is correct, then ...
September 27, 2006 by jessica

Algebra 2
The Denominator of a fraction exceeds the numerator by 4. When 3 is added to both the numerator and denominator, the fraction becomes 4/5. Find the fraction.
October 10, 2012 by Larry

algebra
the numerator of a fraction is 5 less than the denominator.if 1 is added to both the numerator and the denominator the fraction becomes 2/3. find the fraction
November 22, 2012 by abdul basit

Maths
The numerator of a fraction is 2 less than its denominator. If 3 is substracted from the numerator and from the denominator, the new fraction obtainded is 3/4. Find the fraction
January 26, 2015 by Deron

Algebra
In a certain positive fraction \frac{a}{b} , the numerator is 2 less than the denominator. If the numerator and denominator are interchanged, the fraction is increased by 1 \frac{1}{15} . Find a + b .
March 12, 2013 by John

MATH
HOW DO LEAST COMMON MULTIPLES WORK. IT SAYS THERE IS A PROBLEM TO SOLVE BUT MY MOM AND I CAN'T FIND IT. THEY CIRCLED BOTH 2'S AND 3'S. The least common multiple of 2 and 3 is six. The least common multiple of 12 and 6 is 12. # noun: the smallest multiple that is exactly ...
January 2, 2007 by MORGAN

Basic Math
A student claims that 2/3 = 6/7 because if you add 4 to both the top and the bottom of a fraction, the fraction does not change. How do you respond? I am a bit confused. Don't you need to have a common denominator?
February 6, 2011 by Jordan

Algebra
-9+3w/11 divided by 25w-75/121 Do I need a Common denominator? Would it be 121 as 11x11 is 121? Do I then multiply the numeratos- -9+3w by 11 or do I do the addition of -9+3w for-12w?
January 23, 2008 by Marysvoice

basic algebra
the numerator of a certain fraction is four less then the denominator, if the numerator is doubled and the denominator is diminished by two, the sum of the original fraction and the new one is three. find the original fraction
February 8, 2016 by kristina

Maths
When the numerator and denominator of a fraction are each increased by 5, the value of the fraction becomes 3/5 When the numerator and denominator of that same fraction are each decreased by 5, the fraction is then 1/5 Find the original fraction. (Hint: Let the fraction be p/q...
November 13, 2010 by Jannie

physics
calculate the speed of the pendulum at its lowest point if its PE is 5J at its heighest point and has a total mass of 1kg. 5 Joules = (1/2) M V^2 at lowest point. Solve that equation for V at lowest point.
June 16, 2007 by Sweety

Math
Write each of the following as a common fraction or mixed number. Write your answer in lowest term 15.35
February 19, 2008 by Trina

math
Write the following as a common fraction or a mixed number. Write your answer in lowest terms. 0.44
October 11, 2008 by Trac

math
Write the following as a common fraction or mixed number. Write your answer in lowest terms. 0.44
June 21, 2009 by Sandy

Math
Chester and Kelsey were given a box of candy to sell. Each box of candy had 24 individual packages inside. Chester sold 1/4 of the candy in the box and Kelsey sold 3/8 of the candy in the box. Which of the following describes how to find the total number of packages That ...
November 9, 2012 by Jerald

maths
the numerator and denominator of a fraction are in the ratio 3:2 if three is added to the numerator and three is subtracted from the denominator a new fraction is formed whose value is 9/4 find the original fraction?
August 23, 2015 by vinit

Algebra--One Quick Question
31. Determine whether the sequence 7, 21, 35, 49 is geometric. If so, find its common ratio. a. no b. yes, common ratio of 14 c. yes, common ratio of 12 B? Thanks -MC
June 18, 2010 by mysterychicken

6th grade math
I still do not understand this problem? find a number such that when added to the numerator and denominator of 2/11 yields a fraction equivalent to 1/2? thanks If you add 7 to the numerator and 7 to the denominator you get 9/18. 9/18= 9x1/9x2 = 1/2 It means add the same number...
March 8, 2007 by vince

Math / Fractions
I have 3 mixed fractions 2 1/4 , 1 1/2 , 3 5/8 Now I already turned them into improper fractions. 9/4 , 3/2 , 29/8 But I'm a little confused on how to get the common denominator.. Is it 8? or do I multiply their factors?
January 2, 2016 by Slave

Math
Jack says that once you have a common denominator you are ready to subtract two mixed numbers. What other step might be necessary before you can subtract? Give an example.
December 9, 2014 by Jamie

Math
Prove that (xt+yr)/yt is already in lowest terms, b and d have no common prime factor. Note that x/y and r/t are fractions in reduced terms.
September 29, 2013 by John

Mathematics
The numerator of a fraction is two less than its denominator. When both numerator and denominator are increased by 3, the fraction is increased by 3/20. Find the original fraction. Explain your solution
October 22, 2011 by JP

St.george high school
The numerator of a fraction is 8 less than the denominator.when 6 is added to the numerator and 10 is added to the denominator,the value of the fraction is unchanged.find the original fraction.
November 4, 2012 by Lynn

algebra
The denominator of a fraction is 4 less than the numerator .If the denominator is doubled and the numerator is increased by 6,the sum of the original fraction and the new one is 3 .Find the original fraction.
September 18, 2015 by vincent

Physics
A child of mass m sits in a swing supported by two chains, each of length R. The tension in each chain at the lowest point is T. Find the force of the seat on the child at the lowest point
October 12, 2011 by Kari

Calculus/College Algebra
I'm so lost. We're working on limits for this assignment and I get that, but my difficulty lies in breaking down the original problem. The problem is: Find the limit: lim (x->5) The numerator is (the square root of 9-x) -2 and the denominator is x-(the square root of x+20...
February 7, 2007 by Amy

math
write the pair of the fractions as a pair of fractions with a common denominator : a.) 2/4 and 7/8. b.) 3/10 and 1/2. my answer for the a.) is 16/32-28/32. for b.) is 6/20-10/20 please let me know is my answers is right or not
January 6, 2014 by Anonymous

math
I need help on how to use a common denominator to write an equivalent fraction for each fraction?number 1 is 1/2,1/3 and number 2 is 7/8,3/10 please help
March 13, 2014 by sam

General Calculus Question
How do you solve a limit when it approaches infinity and there is a square root in the denominator? say the highest power is x^2 in both the numerator and denominator.
December 8, 2014 by Anonymous

Math
Which is True? A 3/5 > 1/2 B 1/2 < 4/9 C 5/11 > 1/2 D 1/2 > 5/8 How do I determine? Thanks for the help! The shortcut for doing these is as follows: Cross-multiply by multiplying the numerator of the first times the denominator of the second. Then multiply the ...
February 18, 2007 by Mikayla

math
Solve this plxxx The numerator of a fraction is 2less than it's denominator.when both numerator and denominator are increased by 3,the fraction is increased by 3/20.find the original fraction.
January 22, 2016 by Ali

math
how do you solve this type of math problems that indicates to perform the indicated operations for 3 and 3/4 divided by 1 and 3/8 convert the whole numbers into fractions. 3 3/4 = 15/4 1 3/8 = 11/8 to divide 15/4 by 11/8 invert the denominator and multiply. so 15/4 x 8/11. ...
December 4, 2006 by jasmine20

math
Which is heavier 9 5/8 lbs or 9 3/4 lbs. common denominator, 8 . Therefore calcultion that 9 3/4 would be 1/8 heavier!
March 11, 2011 by JUNIOR C

Math
Outside temperature over a day can be modelled as a sinusoidal function. Suppose you know the high temperature for the day is 87 degrees and the low temperature of 63 degrees occurs at 5 AM. Assuming t is the number of hours since midnight, find an equation for the temperature...
September 2, 2014 by Holly

advance functions gr 12
use the asymptotes and intercepts to make a quick sketch of the function f(x)= x-2 (numerator) x+4(denominator) and its reciprocal f^r = x+4 (numerator) x-2 (denominator) on the same set of axes. b) describe the symmetry in the graphs in part a) c) determine the intervals of ...
April 1, 2013 by james

advance functions gr 12
use the asymptotes and intercepts to make a quick sketch of the function f(x)= x-2 (numerator) x+4(denominator) and its reciprocal f^r = x+4 (numerator) x-2 (denominator) on the same set of axes. b) describe the symmetry in the graphs in part a) c) determine the intervals of ...
April 2, 2013 by james

Math advance functions gr 12
use the asymptotes and intercepts to make a quick sketch of the function f(x)= x-2 (numerator) x+4(denominator) and its reciprocal f^r = x+4 (numerator) x-2 (denominator) on the same set of axes. b) describe the symmetry in the graphs in part a) c) determine the intervals of ...
April 1, 2013 by james

Math - Algebra
Solve the inequality. n-1/3n < n-4/3n-4 (it's actually less than or equal to) My first instinct is to multiply 3n, but that'll just give me squares and makes it harder to solve. I also thought about getting a common denominator, but I'm not sure. Thank you!
December 29, 2008 by Momo

math/algebra
Subtract: express your answer in simplest form. 2/5 - y/y-2 answers a)-3y-2/y-2 b) -3y -2/5(4-2) c) -3y-4/5(y-2) d) -3y-4/y-2 The way you have written the problem, is 2/5 minus y^3. I dont think that is what you meant. Please use grouping symbols on fractions () or [] The way ...
July 15, 2007 by Diana

College Algebra
Simplify the expression: (6ax4)^2(2x)^-2 I will be happy to critique your work or thinking on this. I will be happy to critique your work or thinking on this. Note that this is like a fraction with (2x)^2 in the denominator and (6ax^4)^2 in the numerator. You will get some ...
July 7, 2007 by Rey

Algebra
Rationalize V stands for square root 3/V2 3/V2 x V2/V2 = 3V2/V2V2= 3V2/V4 =3V2/2 Answer 3V2/2 6V2/V3 6V2/3 x V3/V3 =6V2V3/V3V3 = 6V6/3= 2V6 My book gives these two examples. In the first problem you multiply the 2 in the denominator and get 4. It the second problem the 3 in ...
June 19, 2009 by G

Algebra
Can someone verify if my answers are correct? Solve. 1/x+6-1/x-6 My answer is: -12/x^2-36 Solve. 1/x+5+2=5/x+5 My answer is: -3 Subtract. Express your answer in simplest form. 13x/30-4x/15 My answer is: x/6 Can someone verify if my answers are correct? Solve. 1/x+6-1/x-6 My ...
July 12, 2007 by Need Help

Algebra
the denominator of a fraction exceeds the numerator by 7, if the numerator is increased by 3, and the denominator is increased by 5, the resulting fraction equals 1/2. Find the original fraction.
March 22, 2016 by Scotch

basic math
In my book A bread piece calls for 3 1/4 cups of flour if you only have 2 1/8 cup. How much more flour is needed? 3 1/4 -2 1/8= 13/4 - 17/9 how does it equal 13/4 can someone show me that part? I thought I knew how to subtract fractions but I dont get it. 3 1/4 - 2 1/8 = 13/4...
August 6, 2007 by chrissy

AP Physics
A 35kg child sits in a swing supported by 2 chains, each 3.7 m long. If the tension in each chain at the lowest point is 274 N find the child's speed at the lowest point. (Neglect the mass of the seat). I'm not sure what equations to use to set this up
October 27, 2015 by Chevy

algebra
How do you factor out the greatest common factor? 1. 96x^9y^8+60x^2y^6-84x^4y^4 2. 13m^2-22r^3 3. 24m^8+48m^5-36m^2 1. In the coefficients look for the largest number which evenly divides into all the coefficients of the given terms 2. Variables must have the same base, the ...
April 23, 2007 by shea

Calculus
Hi. In an integration solution, the integral of (1/(sqrt (8-u squared)) is written as arcsin(u/sqrt 8), but I dont see how they got it. When I did it I got (1/8)*(arcsin(u*sqrt8)). What I did was take sqrt8 common in the denominator to get it in the form sqrt(1-u sq.) and then...
December 5, 2009 by O_o Rion

College Mathematics. 3
(3t+1)/5=(t+7)/10+(t-5)/10 I solved this question through the linear equation simplification timing both sides by the least common denominator. 5 Once I did the the result was > 3t+1= 2t+14+2t-10 T= 3 However the real answer is t=0 Where am I going wrong? How am I supposed ...
September 29, 2011 by HM

Maths
the 5th, 9th and 16th term of an AP are consecutive terms of the GP. Find. 1. the common ratio of the GP 2. given that the 13th term of the AP is 200, find the common difference of the AP.
January 19, 2016 by Elisha

Math
2. Find the LCM and GCD of (2y^2 - 3a^2)x + (2a^2 - 3x^2)y and (2a^2 + 3x^2)y + (2y^2 + 3a^2)x 3.Find m if the polynomials (x^2 - 2mx + 2) and (3x^2 - mx - 4) have a common linear factor 4. The ramainder on dividing 121^n - 25^n + 1900^n - (- 4)^n by 2000 is ___________ 5. ...
November 17, 2010 by Sashaank

chemistry
Suppose you are given a list of solutions (all with nonvolatile solutes) and their concentrations. You pick out the one with the lowest freezing point. It should also have (pick all that apply): the lowest boiling point the highest osmotic pressure the lowest solvent vapor ...
September 8, 2010 by Megan

Physics
A walker's speed, v, is proportional to the ratio of his leg length, L, and the period of the repeating motion of his legs, T, that is, v ∝ L/T. If the period is measured to be proportional to Lp, where p = 3/5, what power of L must the speed be proportional to? Enter ...
October 27, 2015 by Jen

math 117/algebra
The combined resistance of two resistors R_(1 amd R_2 )in a parallel circuit is given by the formula R_(r= 1/(1/R_1 + 1/R_2 )) Simplify the formula. Help what is this talking about and how do I work it? find R as a function fo r`1 and r2. 1/R= 1/r1 + `1/R2 R= ??? Get a common ...
July 11, 2007 by Diana

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