Simplfing Fractions

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.

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