Friday

August 26, 2016
Total # Posts: 35,558

**stats**

number of possible 5-digit pins = 3x3x3x3x3 = 243 prob(same) = 1/243
*June 1, 2016*

**math plz help ;-;**

slope is (-7-8)/(1+4) = -15/5 = -3 so y = -3x + b plug in one of your points, I picked (-4,8) : 8 = -3(-4) + b ---> b = -4 so y = -3x - 4 now, how easy was that?
*June 1, 2016*

**Math - system of eqns**

1 1 1 | 6 -1 -2 3 | 1 3 -4 4 | 5 1 1 1 | 6 0 -1 4 | 7 from: add #1 and #2 0 7 -1 | 13 from #3 x 1 - #3 1 1 1 | 6 0 -1 4 | 7 0 0 27| 62 from #2 x 7 + #3 1 1 1 6 0 1 -4 -7 switch signs 0 0 1 62/27 divide by 27 so x3 = 62/27 now back substitute x2 - 4(62/27) = -7 x2 = 248/27 -7...
*June 1, 2016*

**math**

let the times for the 3 subjects be 2x, 3x and x hrs each 2x+3x+x = 8 6x=8 x = 4/3 science : 2(4/3) = 8/3 hrs or 2 hrs and 40 minutes Math : 3(4/3) = 4 hours Lit : 4/3 hrs or 1 hour and 20 minutes check: 2:40 + 4:00 + 1:20 = 6:00
*June 1, 2016*

**Radicals**

not sure of your notation. does ^3 root -192 supposed to mean the cuberoot of -192 ? if so , (-192)^(1/3) = (-64)^(1/3) * (3^(1/3) = -4 (3)^(1/3) or -4 cuberoot (3) -6 exponent 3root 13 ?? = (-6)^3 √13 ???
*May 31, 2016*

**Adding and subtracting mixed numbers**

I would do it this way: (4 1/8 + 6 1/4) - 2 1/2 first of all, there is no need for the brackets in this case secondly, I change all my mixed fractions to workable fractions = 33/8 + 25/4 - 5/2 LCD is 8 = 33/8 + 50/8 - 20/8 = 63/8 or 7 7/8 mixed numbers are "nice" to ...
*May 31, 2016*

**Algebra**

First of all: you don't have an equation to solve are you simplifying? Your run-ons of "over" have to bracketed to establish priority e.g. is it ( (1+1/x)/x ) / (1/(x-1) ) or ( (1+1/x)/x ) / (1/x-1) ) or ...
*May 31, 2016*

**math plz help ;-;**

easiest way: for the y-intercept, let x = 0 , (can be done mentally) so -3y=12 ----- > y = -4 You are probably using the equation in the form y = mx +b, where b is the y-intercept, so change your given equation to that form 2x - 3y = 12 -3y = -2x + 12 divide by -3 y = (2/3)...
*May 31, 2016*

**Maths (quadratic equation) need help**

base ---- x height ---2x-3 area of triangle = (1/2) base x heigh (1/2)(x)(2x-3) = 10 carry on
*May 31, 2016*

**Maths (quadratic equation) need help**

using their hint: let the numerator of original fraction be x then the denominator is 2x+1 so the original fraction is x/(2x+1) condition stated: x/(2x+1) + 2 1/10 = (2x+1)/x x(2x+1) + 21/10 = (2x+1)/x multiply each term by 10x(2x+1) , the LCD 10x^2 + 21x(2x+1) = 10(2x+1)^2 ...
*May 31, 2016*

**Math - Vectors**

a) u = (-1, 2, -1) , v = (2, -1, 0) , w = (1, 1, -1) b) you want the cross-product of u and v, that is, a vector which is perpendicular to both u and v I don't know which method you have learned, but you should get (1, 2, 3) c) the normal to the triangle is (1,2,3) so the ...
*May 31, 2016*

**Math - Year 10 - Probability**

I can't solve the question, because there was no question.
*May 31, 2016*

**math help**

1,127.5 milligrams = 1.1275 grams ahhh, the beauty of the metric system !
*May 31, 2016*

**maths**

When I answered this question there was another solution after Steve's which has now been deleted. I only completed Steve's solution to correct that other posting.
*May 31, 2016*

**maths**

from Steve's ... 1/x + 1/y = 7/20 times 20xy, the LCD 20y + 20x = 7xy 20(y+x) = 7xy 20(14) = 7xy 40 = xy -----> y = 40/x plug into the first: x + 40/x = 14 x^2 + 40 - 14x = 0 (x-10)(x-4) = 0 x = 10 or x = 4 if x = 10, y = 40/10 = 4 if x = 4 , y = 40/4 = 10 the numbers ...
*May 31, 2016*

**Math Calculus I**

your f ' (x) is correct but not complete f ' (x) = (9*(cos^2(x)+sin^2(x)))/(3cos(x)+sin(x))^2 remember that sin^2 x + cos^2 x = 1 f '(x) = 9/(3cosx + sinx)^2 so when x = π/6 , f'(π/6) = 9/(3√3/2 + 1/2)^2 = appr .93769 this is the slope of the ...
*May 30, 2016*

**math**

Assuming you made your sketch, angle SOT + angle E = 180° , (since the angles at S and T are each 90° ) angle SOT + 78 = 180 angle SOT = 102° so the arc SOT = 102/360 of the circumference = 17/60 of the circumference
*May 30, 2016*

**Math - volume about y axis**

Makes no sense to me neither. f(x) = x^2 - 1 is a parabola opening upwards, so when we revolve it about the y-axis we have it open-ended above. We need a closed region to revolve. Did you mean the region below the x-axis ?
*May 30, 2016*

**Algebra 1**

length = 4x-3 Width = x-4 2W + 2L = perimeter 2(4x-3) + 2(x-4) = 84 8x - 6 + 2x - 8 = 84 10x = 98 x = 9.8
*May 30, 2016*

**Trigonometry**

sketch a right-angled triangle . since cosØ = 2/5 = x/r x^2 + y^2 = r^2 4 + y^2 = 25 y^2 = 21 x = ±√21 case 1: if x = +√21 cosØ = 2/5 , sinØ = √21/5 cos 2Ø = cos^2 Ø- sin^2 Ø = 4/25 - 21/25 = -17/25 case 2: if ...
*May 30, 2016*

**Math..help**

you should memorize the pattern for squaring a binomial: (a - b)^2 = a^2 - 2ab + b^2 so (3a - 7/9)^2 = 9a^2 - 42/9 a + 49/81 = 9a^2 - (14/3) a + 49/81
*May 30, 2016*

**Math (Polar to Cartesian Equations)**

secØ = r/x , cscØ = r/y so r^2 = 4(r/x)(r/y) r^2 = 4r^2/(xy) 1 = 4/(xy) xy = 4
*May 30, 2016*

**math**

just sub into the basic formula: amount = 400(1.07)^t
*May 30, 2016*

**Math help!**

#5 7^4/7^2____ 49 7^2 ______ 49 49 _____ 49 care to re-evaluate your answer? #6 –2r(8r + 5) = -16r^2 - 10r #7 correct #8. (2y – 3) (3y – 2) = 6y^2 - 4y - 9y + 6 = 6y^2 - 13y + 6 mmmmhhh, 1 out of 4 correct, somebody needs more studying and review.
*May 30, 2016*

**math**

arc cd=90° ?? this makes no sense, since arc length is measured in linear units , not degrees Are you saying that the arc cd subtends a 90° angle at the centre? If so, then r^2 + r^2 = 12^2 2r^2 = 144 r^2 = 72 r = 6√2 area of whole circle = 72π inches^2 area...
*May 30, 2016*

**Math**

correct
*May 30, 2016*

**math**

width --- x length --- x+4 solve for x x(x+4) = 117 hint: the quadratic factors nicely.
*May 30, 2016*

**Math**

Poorly worded question. Assuming her position is at the origin, and assuming by "path of ball" you mean the height of the ball, and assuming the net is at (20,10), and assuming the ball lands 5 ft beyond the net, we could have .... height = ax(x-25) subbing in (20,10...
*May 30, 2016*

**algebra**

300 ft/2.92 seconds = (300/5280) miles / (2.92/3600) hrs = (300/5280)(3600/2.92) mph = 70.05 mph = appr 70 mph
*May 30, 2016*

**math**

calculate the distance for different values of t e.g. t = 0, D(0) = -1.5(-8) + 9 = 21 t = 1, D(1) = 19.5 ... t = 5 , D)5) = 13.5 .. t = 8 , D(8) = 9 .. t = 12 , D(12) = 3 t = 15 , D(15) = -1.5 This question does not make any sense to me
*May 30, 2016*

**maths**

I don't understand your question. Please proofread and repost. Where does C suddenly come from ?
*May 30, 2016*

**Math**

L --- linear N --- non-linear xy = -9 --- N y = 3x --- L x + 7 = y --- L y = x - 4 --- L y = x^2 --- N x + y - 20 = 2x --- L 1/2x = y ---- L y = 5/x ---- N y = 30 - x^2 ---- N Did you notice why some are L and some are N ?
*May 30, 2016*

**Math**

Make a sketch to see that r = 5, h = 3 then s^2 = 5^2 + 3^2 = 34 slant height = √34 cm circumference of base of cone = 2π(5) = 10π cm This becomes the arc-length in a circle of circumference of 2π√34 let the angle of the sector be Ø arc = r&...
*May 30, 2016*

**math plz help ;-;**

Since both equations contain 2x, the easiest way would be elimination, thus subtract them: -4y = -2 y = -2/-4 = 1/2 sub into the first: 2x - 5(1/2) = -1 2x = 5/2-1 = 3/2 x = 3/4 ---------> x = 3/4 , y = 1/2 #2 y=(3/5_x-1 y=6/10x+3 ----> y = (3/5)x + 3 since you have two ...
*May 30, 2016*

**math**

(1.4*10^1)(8*10^4) = 11.2 * 10^5 = 1.12 * 10^6
*May 29, 2016*

**Geometry**

tan 43° = height/250 solve for "height"
*May 29, 2016*

**CORRECTION - Maths , logarithms**

#1 answer is incorrect 2^x * 6^x = log 14 14^x = log 14 now take logs of both sides, and use log rules x log14 = log(log14) x = log(log14)/log14 = appr .05168 it is easy to show that x = 1 is not a solution to the question since 14^1 ≠ log14 #2 2^2x+1 - (9)2^x = -4 the ...
*May 29, 2016*

**Algebra**

number of generals (student?) --- x , x ≥ 300 number of adults ----- y , y ≥ 500 ad cost = .5x + 1y , where .5x+y ≤ 400 profit = 6x + 9y - .5x - y = 5.5x + 8y The question cannot be answered e.g. If we allow the min of each x = 300, y = 500 profit = 5.5(300...
*May 29, 2016*

**algebra**

Just translate into math: shortest side --- x longest side ---- x+7 remaining side --- x+2 solve: x + x+7 + x+2 = 45
*May 29, 2016*

**Math**

(2/5)x + 15 = 27 solve for x
*May 29, 2016*

**Math**

let the 3 consecutive odds be n, n+2, and n+4 n+n+2+n+4=69 3n = 63 n = 21 They are 21, 23, and 25, with 23 as the prime one
*May 29, 2016*

**Maths**

I see a recursive formula: term(n) = term(n-1) + (n-1)^2 , for n > 1 , term(1) = 0 term(1) = 0 term(2) = 0 + 1^2 = 1 term(3) = 1 + 2^2 = 5 term(4) = 5 + 3^2 = 14 term(5) = 14 + 4^2 = 30 term(6) = 30 + 5^2 = 55
*May 29, 2016*

**Math**

average score of first three test is 90 ----> sum of those 3 tests was 270 average score of two test is 89 ---> sum of those 2 tests = 178 avg of 5 tests = (270 + 178)/5 = 89.6
*May 28, 2016*

**Math**

The volumes of two similar objects are proportional to the cube of their sides so vol1 : vol2 = 2.6^3 : 3.4^3 = 13^3 : 17^3 = 2197 : 4913 note: 2.6/3.4 = 26/34 = 13/17
*May 28, 2016*

**algebra**

If you meant: 7a^4 b , then the degree would be 5
*May 28, 2016*

**Algebra**

base ----- x cm height ---- 2x-4 cm area of triangle = (1/2) base x height (1/2)(x)(2x-4) = 48 x(2x-4) = 96 2x^2 - 8x - 96 = 0 x^2 - 4x - 48 = 0 (x-8)(x+6) = 0 x = 8 or x = -6, the latter is inadmissable base is 8 cm height is 12 cm
*May 28, 2016*

**Maths**

length of trail ---- x miles x/15 - x/20 = 8/60 times 60 , the LCD 4x - 3x = 8 x = 8 the trail is 8 miles long check: time at 20 mph = 8/20 hrs = 24 minutes time at 15 mph = 8/15 hrs = 32 minutes for a difference of 8 minutes
*May 28, 2016*

**Calc**

Because of summetry, we only need to look at the first quadrant Area of whole thing in quadrant I = ∫(16 - 4x^2) dx from 0 to 2 = [16x - (4/3)x^3] from 0 to 2 = 32 - (4/3)(8) - 0 = 64/3 So the area created by y = b must be 32/3 the intersection of y = b and y = 4x^2: 4x^...
*May 27, 2016*

**Go with Steve - Calculus**

My answer is gibberish I read it as area not volume, the irony is that I used to stress "Read the question carefully at least three times"
*May 27, 2016*

**Calculus**

Then you simply have area = ∫ (5 - 1/x) dx from 1 to 4 = [5x - lnx] from 1 to 4 take over after you found your answer , look at http://www.wolframalpha.com/input/?i=area+between+y+%3D+5+and+y+%3D+1%2Fx+from+1+to+4
*May 27, 2016*

**Calculus**

area = ∫ 1/x dx from 1 to 4 = [lnx] from 1 to 4 = ln4 - ln1 = ln4 - 0 = appr 1.3863 confirmation: http://www.wolframalpha.com/input/?i=%E2%88%AB+1%2Fx+dx+from+1+to+4 b) not sure about the y = 5 Are we rotating about y = 5 instead of the x-axis? Do we still have x = 1 to ...
*May 27, 2016*

**math**

do we know how many bottles in a case?
*May 27, 2016*

**MATH - CALC**

f(x) = x^3 - 3x^2 = x^2(x-3) You should be familiar with the general shape of y = 1x^3 + ..... yours crosses at x = 3 and since you have a double root at x = 0, it touches the x-axis at x = 0 find f'(x) and f''(x) , that should be easy when f'(x) is positive, ...
*May 27, 2016*

**math**

really? You are studying the above topic and you are asking this question? Sorry, but .....
*May 26, 2016*

**math**

"first term in an arithmetic sequence is 15" ---> a=15 "the tenth term is 69" ---> a+9d = 69 sub in a = 15 to find d then evaluate a + 3d
*May 26, 2016*

**math**

I will assume d is the diameter. so r = 4, h = 12 V = (1/3)π r^2 h plug in your values
*May 26, 2016*

**Math **

what is 1.35(29.50) ?
*May 26, 2016*

**math**

speed of plane without wind ---- x km/h speed of wind --------- y km/n 5600/(x-y) = 8 700/(x-y) = 1 x-y = 700 ** 9900/(x+y) = 9 1100/(x-y) = 1 x + y = 1100 *** add ** and *** to find x then sub back into **
*May 26, 2016*

**math**

Very very unsafe placement of a ladder.
*May 26, 2016*

**Ratios math**

cars : SUV's = 4:1 = 16:4 SUV's : Minivans = 4:5 now that I have a common "4" for the SUV's in both, I can say cars : SUV's : minivans = 16 : 4 : 5 or = 16x : 4x : 5x but 5x = 20 x = 4 so we have 64 cars, 16 SUV's , and 20 minivans for a total of ...
*May 26, 2016*

**Math**

Kiki, I found the 2.5 seconds for you in your previous post. Just sub that value into your equation. then do it again for t = 4 let me know what you got.
*May 26, 2016*

**Math**

what is C(5,2) x C(3,1) ?
*May 26, 2016*

**Math**

equivalent to finding the vertex of the parabola h = -16t^2 + 80t + 6 the t of the vertex is -b/(2a) = -80/-32 = 2.5 seconds
*May 26, 2016*

**math**

@ sad/jeo 6 almost identical questions without any work shown or indication where your problems are. Steve and I have answered 3 of them. Surely you can do the rest by following our methods.
*May 26, 2016*

**math**

if selling at 600 is a loss of 25%, the cost was .75x = 600 x = 800 so make a profit of 25% on the 800 , he should have sold at 800(1.25) = 1000
*May 26, 2016*

**math**

cost of first = 240/1.2 = 200 cost of 2nd = 240/.8 = 300 percentage change = (200+300)/480 = 1.04166.. he made a profit of appr 4.17%
*May 26, 2016*

**precal**

two numbers: x and y xy = 48 ---> y = 48/x and 1/x + 1/y = 1/3 (x+y)/(xy) = 1/3 (x+y)/48 = 1/3 x+y = 16 x + 48/x = 16 x^2 + 48 = 16x x^2 - 16x + 48 = 0 (x-12)(x-4) = 0 x = 12 or x = 4 if x = 12, y = 48/12 = 4 if x = 4, y = 48/4 = 12 The two numbers are 12 and 4
*May 25, 2016*

**Pre-cal**

cos^2 x = 3/4 cosx = ± √3/2 x = 30°, 150°, 210° or 330° in radians: π/6, 5π/6, 7π/6, 11π/6
*May 25, 2016*

**Math**

Your question is not clear at all. Are we first selecting the committees, then picking the president and vp ? number of committees = C(11,5) = 462 to pick a president , then vice president, order does matter, so 11x10 = 110 or P(11,2) if we are picking the pres and vpres from ...
*May 25, 2016*

**algerba**

the usual way to type a power is to use the ^ to show exponents, e.g. x^2 is "x squared" 0 = −2x^2 − 3x + 8 in standard form is 2x^2 + 3x - 8 = 0 so b^2 - 4ac = 9 - 4(2)(-8) = ...... 4(x + 2)^2 = 36 divide both sides by 4 (x+2)^2 = 9 x+2 = ±√...
*May 25, 2016*

**Math/ ratios/ Fractions/ Singapore Math**

Ross' total --- x Holly's amount = 60-x after spending: Holly has (3/4)(60-x) Ross has x-5 given: Holly/Ross = 1/2 (3/4)(60-x) / (x-5) = 1/2 45 - (3/4)x / (x-5) = 1/2 90 - (3/2)x = x - 5 180 - 3x = 2x - 10 190 = 5x x = 38 take over, using my definitions at the top
*May 25, 2016*

**Math/ more ratios**

let the number of pennies they have be 6x , 5x and 7x respectively 6x + 5x + 7x = 754 18x = 754 x = 41.88.. you are right, it makes no sense, it has to be a whole number. I suspect a typo in the question in your text or whatever your source.
*May 25, 2016*

**correction - College Algebra**

You cannot take log of individual terms, you have to take log of both sides. i.e. log (3^n + 9) = 69 but , why not just do this: 3^n = 60 now log both sides, and use log rules: n log3 = log60 n = log60/log2 = appr 3.727 check: 3^3.727 + 9 = 69.01100 , close enough to 69 if you...
*May 25, 2016*

**math**

amount of her money --- x after spending 2/7 of it, she has (5/7)x left then she spends (2/5) of that, or (2/5)(5/7)x total amount spent = (2/7)x + (10/35)x = (2/7)x + (2/7)x = (4/7)x so (3/7)x = 15 3x = 105 x = 35 <------ money she started with check: she spends (2/7)(35) ...
*May 25, 2016*

**school**

Things you learn from Google: http://www.shmoop.com/walk-two-moons/margaret-cadaver.html Ironic: At the top of the webpage it showed an ad for Plagiarism software
*May 25, 2016*

**math**

his cost price = rs 16 so his selling price should be 1.15(16) or rs 18.4 per dozen. But you want the selling price per hundred so : 18.4/12 = x/100 x = 100(18.4)/12 = 153.333... (notice the fact that he bought 1200 eggs did not enter the calculation) check: cost price per ...
*May 25, 2016*

**Calc-Math**

your derivative is wrong, the xy needs a product rule 2y dy/dt + x dy/dt + y dx/dt - 3dx/dt = 0 plugging in our stuff 2 (-4) + 3(-4) + 1(dx/dt) - 3 dx/dt = 0 -2 dx/dt = 20 dx/dt = -10
*May 24, 2016*

**Calculus**

so your equations can be written as y = 1/√x and y = 1/x^2 let's look at their graphs: http://www.wolframalpha.com/input/?i=plot+y+%3D+1%2F%E2%88%9Ax+,+y+%3D+1%2Fx%5E2 ignore the part for x<0 , since in y = 1/√x, x > 0 so let's take horizontal slices ...
*May 24, 2016*

**Financial Math**

clearly repetition would be allowed in passwords, and I would assume we can start with zero as well number of passwords = (10^3)(26^2) = ...
*May 24, 2016*

**Algebra**

youngest ---- x oldest ---- 2x (2x + 12 + 15 + x)/4 = 13.5 3x + 27 = 54 take over
*May 24, 2016*

**Math**

let the point on the line be (x,y) line is y = (4-x)/4 = 1 - (1/4)x area of rectangle: A = xy = x( 1 - (1/4)x) = x - (1/4)x^2 this is a downwards parabola. We need the vertex the x of the vertex is -b/2a = -1/(-1/2) = 2 then y = 1- (1/4)(2) = 1/2 max area = xy = 2(1/2) = 1 ...
*May 24, 2016*

**Math**

a coefficient is simply the number in front of the variable. So it is -7
*May 24, 2016*

**Algrebra Help!**

just plug in n = 1 n = 2 n = 3 n = 4 and evaluate. e.g. n = 3 value is 3(3-2) - 3 = 3(1) - 3 = 0
*May 24, 2016*

**Math**

let the unit digit be x let the tens digit be y the number is 10y + x 10y + x = 2(y-x) 10y + x = 2y - 2x 8y = -3x mmmmhhhh? do you have a typo?
*May 24, 2016*

**German**

#1 Beantwortest du die Fragen ? - Are you answering the questions ? Fragtest du die Fragen? - Had you asked the questions ? Either one would actually be acceptable, depending which idea you were trying to convey. #2 by the process of elimination, I have to say Wir lernen ü...
*May 24, 2016*

**Algebra**

yup!
*May 24, 2016*

**pre-algebra**

agree
*May 24, 2016*

**geometry**

mmmhhh, did you plot your points? Can you see any way they could form a rectangle?
*May 24, 2016*

**math**

You did not specify whether you want degrees or radians. I will do it for degrees. Repeat for radians, make sure to set your calculator to radians 3sec^2 y = 5(1+tany) We know sec^2 A = 1 + tan^2 A 3(1 + tan^2 y) = 5(1 + tany) 3 + 3tan^2 y = 5 + 5tany 3tan^2 y - 5tany - 2 = 0...
*May 24, 2016*

**math**

#1 cos(x+20) = sin(90 - (x+20) ) , one of the basic rules but sinx = cos(x+20) sinx = sin(70-x) arcsin both sides x = 70-x 2x=70 x = 35 check: LS = sin 35 RS = cos(35+20) = cos 55 but cos 55 = sin 35 so all is good tanx = sinx/cosx = cos(x+20)/cosx = (cosxcos20 - sinxsin20)/...
*May 24, 2016*

**Math**

SA = 2lw + 2 lh + 2 wh plug in ....
*May 24, 2016*

**Maths**

let that time be n years 1.02^n = 2 log both sides, then use rules of logs n log1.02 = log2 n = log2/log1.02 etc
*May 24, 2016*

**algebra**

generally called an inverse proportion ? then ... y = k/x if x = 2 , y = 12 12 = k/2 k = 24 y = 24/x
*May 24, 2016*

**linear-equations-in-one-variable**

or - using one variable, as your title suggests width --- x length --- x+4 new width = x+3 new length = x+7 (x+3)(x+7) - x(x+4) = 81 x^2 + 10x + 21 - x^2 - 4x = 81 6x = 60 etc
*May 24, 2016*

**algebra**

typo, you have no 2nd equation
*May 23, 2016*

**Maths (Need Help)**

(2x-3)^2-3x = 4x^2 - 12x + 9 -3x = 4x^2 - 15x + 9) = (x-3)(4x - 3) (x^2-4)+(x+2)^2 = (x-2)(x+2) + (x+2)(x+2) = (x+2)(x-2 + x+2) = (x+2)(2x)
*May 23, 2016*

**Math**

prob =(1/4)(1/2) = 1/8
*May 23, 2016*

**Math**

#1 you have 4 colours and 2 ways to flip a coin so there should be 8 possible outcomes. your choice has only 6 outcomes #2, correct #3, correct #4, no, there are 21 students, 12 of which are boys prob = 12/21 = 4/7 you stated the ratio of girls : boys
*May 23, 2016*

**Maths**

I bet you mean: 4/(a^2 -2a-3) + a/(a-3) + a/(a+1) = 4/( (a-3)(a+1) + a/(a-3) + a/(a+1) = ( 4 + a(a+1) + a(a-3) )/( (a-3)(a+1) ) = (2a^2 - 2a + 4)/( (a-3)(a+1) ) or = 2(a^2 - a + 2)/( a^2 - 2a - 3)
*May 23, 2016*