How do I Simplify this?

Question

a) (3^-12 + 3^-14) / (3^-12 - 3^-14)
b)3^(2m+2) + 3^2m / (3^m + 3^(m+1))

For a: I got 5/4.
For b. I got 2. But I'm not sure about my answers.
i did.. 4m + 2 / 2m + 1 (since the base is common for all of them)

Can somebody check please. Thanks.

Answer 1

A. Correct

= 3^-12(1 + 3^-2) / 3^-12(1 - 3^-2)
= (10/9) / (8/9)
= 10/8
= 5/4

B. Not sure if you are right - see what I have done below.
I have assumed that everything before the '/' is the numerator - I think that is correct.

= 3^(2m) ( 3^2 + 1 ) / 3^m ( 1 + 3 )
= 3^(2m - m) ( 10 / 4 )
= 5/2 x 3^m

Answer 2

The trick here is to try to express everything in terms of 3^-12. It isn't as hard as it sounds.
In the first problem , if we let 3^-12 = u, then the numerator becomes u+ u/3^2 or 9/8 u. The denominaor becomes 8/9 u. Then we have
9/8 u / 8/9 u or 81/64!!!
You should be able to do the same with the second example.

Answer 3

The first answer is correct. Without working out all the details, I don't like the second answer -- there should be an m in it somewhere.