Three problems I need to know if I am correct or not if not I will place how I got the answer and maybe some one can show me where I messing up aT
Simplify
1+2/3 over top 2+1/2
My answer
was 2/3 to me it does not seem right If I am wrong please let me know i will put all the steps I did to get this and maybe you can help me see where I did it wrong
2nd question
m^5/4 over top of m^7/16
My answer was 4/m^3
3rd question
3/x-5 +1 over top of 1- 4/x-5
My answer is x-2/x-9
1+2/3 over top 2+1/2
My answer
was 2/3 to me it does not seem right If I am wrong please let me know i will put all the steps I did to get this and maybe you can help me see where I did it wrong
I agree with the answer of 2/3 if the problem is([1 + (2/3)]/[2 + (1/2)] =
2nd question
m^5/4 over top of m^7/16
My answer was 4/m^3
For (m5/4)/(m7/16) = I get the 4 but not over m3.
3rd question
3/x-5 +1 over top of 1- 4/x-5
My answer is x-2/x-9 I can't tell what the problem is without parentheses.
Lets do the numerator: 1+ 2/3= 5/3
Now the denominator: 5/2
5/3 / 5/2 which is the same as (remember that multiplying the reciprocal is the same as divideing..
5/3 * 2/5 = 5*2/3*5= 2/3 So it is right. Good work.
On the second,
m^5/4 divided by m^7/16 changes to
M^5/4 * 16/m^7 or
m^5/4 * 16* m^-7
4 m^-2 or 4/m^2
Last:
3/(x-5) + 1 or (3+x-5)/(x-5) is numerator.
Now, for denominator,
that changes to (x-5 -4)/(x-5) or
(x-9)/(x-5)
so numerator /denominator changes to a multiply by
numerator * (1/denominator) or
(3+x-5)/(x-5) * (x-5)/(x-9) or
(x-2)/(x-5) and you are correct.
Find of 12. Express your answer in simplest form.
1. Simplify (1 + 2/3) / (2 + 1/2):
- First, find the common denominator of 3 and 2, which is 6.
- Rewrite the fractions using the common denominator: (1 * 6/6 + 2/3) / (2 * 3/3 + 1/2)
- Simplify the fractions: (6/6 + 2/3) / (6/3 + 1/2)
- Add the fractions: (6 + 2/3) / (6/3 + 1/2)
- Combine the whole numbers with the fractions: (6 + 2/3) / (2 + 1/2)
- Convert the mixed numbers to improper fractions: (6 + 2/3) / (2 + 1/2) = (18/3 + 2/3) / (4/2 + 1/2)
- Add the fractions again: (20/3) / (5/2)
- Invert the second fraction and multiply: (20/3) * (2/5) = 40/15
- Simplify the fraction if necessary: 40/15 = 8/3
So the simplified form of (1 + 2/3) / (2 + 1/2) is 8/3.
2. Simplify (m^5/4) / (m^7/16):
- Divide the numerators and denominators: (m^5/4) / (m^7/16)
- Multiply by the reciprocal of the second fraction: (m^5/4) * (16/m^7)
- Simplify the expression: (m^5 * 16) / (4 * m^7)
- Multiply the numerical coefficients: 16/4 = 4
- Subtract the exponents of the variable: m^(5-7) = m^(-2)
- Rewrite the result: 4/m^2
So the simplified form of (m^5/4) / (m^7/16) is 4/m^2.
3. Simplify (3/(x-5) + 1) / (1 - 4/(x-5)):
- Simplify the numerator: 3 + (x-5) = x-2
- Simplify the denominator: 1 - (4/(x-5)) = (x-5) - 4/(x-5)
- Combine like terms in the denominator: (x-5) - (4/(x-5)) = (x-5) - 4/(x-5)
- Multiply the fractions by the common denominator (x-5): (x-2)/(x-5) / [(x-5) - 4/(x-5)]
- Simplify the expression: (x-2)/(x-5) / (x-5 - 4/(x-5))
- Combine the fractions: (x-2)/(x-5) / [(x(x-5) - 4)/(x-5)]
- Simplify the expression: (x-2)/(x-5) / [(x^2 - 5x - 4)/(x-5)]
- Multiply by the reciprocal of the denominator: (x-2)/(x-5) * [(x-5)/(x^2 - 5x - 4)]
- Cancel out the common factors: (x-2)/(x^2 - 5x - 4)
So the simplified form of (3/(x-5) + 1) / (1 - 4/(x-5)) is (x-2)/(x^2 - 5x - 4).
1. Simplifying (1 + 2/3) / (2 + 1/2):
To simplify this expression, we first need to find the common denominator for the fractions in the numerator and the denominator. In this case, the common denominator is 6.
1 + 2/3 can be rewritten as 3/3 + 2/3, which simplifies to 5/3.
2 + 1/2 can be rewritten as 4/2 + 1/2, which simplifies to 5/2.
Now we have (5/3) / (5/2). To divide fractions, we multiply the first fraction by the reciprocal of the second fraction.
(5/3) * (2/5) = 10/15 = 2/3
Therefore, the simplified expression is 2/3.
2. Simplifying (m^5/4) / (m^7/16):
To simplify this expression, we can use the rule of division, which states that when dividing two exponential expressions with the same base, we subtract the exponents.
(m^5/4) / (m^7/16) can be rewritten as (m^5/4) * (16/m^7).
Simplifying further, we can multiply the coefficients and subtract the exponents.
(m^5 * 16) / (4 * m^7) = (16m^5) / (4m^7)
We can simplify this by dividing both the numerator and denominator by 4.
16/4 = 4
m^5/m^7 = 1/m^2
So, the simplified expression is 4/m^2.
3. Simplifying (3/(x-5) + 1) / (1 - 4/(x-5)):
To simplify this expression, we need to find the least common denominator (LCD) for the fractions in the numerator and denominator.
The LCD of (x-5) and (x-5) is (x-5).
Now we can rewrite the expression with the common denominator.
(3/(x-5) + 1) / (1 - 4/(x-5)) can be rewritten as ((3 + (x-5))/(x-5)) / ((1(x-5) - 4)/(x-5)).
Simplifying further, we can combine like terms in the numerator and simplify the denominator.
((x-2)/(x-5)) / ((x-4)/(x-5))
To divide fractions, we multiply the first fraction by the reciprocal of the second fraction.
((x-2)/(x-5)) * ((x-5)/(x-4)) = (x-2)/(x-4)
Therefore, the simplified expression is (x-2)/(x-4).