SOLUTION: Simplify. Assume all variables represent nonzero integers. 3^(q+3) - 3^2(3^q) ----------- ------ 3(3^q+4) The book's answer was 2/27 but I don't know how to solve it.

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Simplify. Assume all variables represent nonzero integers. 3^(q+3) - 3^2(3^q) ----------- ------ 3(3^q+4) The book's answer was 2/27 but I don't know how to solve it.       Log On


   

Question 975631: Simplify. Assume all variables represent nonzero integers.
3^(q+3) - 3^2(3^q)
------------------
3(3^q+4)
The book's answer was 2/27 but I don't know how to solve it.
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!

%283%5E%28q%2B3%29+-+3%5E2%283%5Eq%29%29%2F%283%283%5E%28q%2B4%29%29%29

We add the exponents of 3 in the SECOND terms on top, which are 2 and q,
we get:

%283%5E%28q%2B3%29+-+3%5E%282%2Bq%29%29%2F%283%283%5E%28q%2B4%29%29%29

Change the 3 in the bottom to 31

%283%5E%28q%2B3%29+-+3%5E%282%2Bq%29%29%2F%283%5E1%283%5E%28q%2B4%29%29%29

Then add the exponents of 3 in the bottom:

%283%5E%28q%2B3%29+-+3%5E%282%2Bq%29%29%2F%283%5E%28q%2B5%29%29

Then make this into two fractions:

%283%5E%28q%2B3%29%29%2F%283%5E%28q%2B5%29%29%22%22-%22%22%283%5E%282%2Bq%29%29%2F%283%5E%28q%2B5%29%29

Subtract exponents of 3 in the fractions:

3%5E%28%28q%2B3%29-%28q%2B5%29%29%22%22-%22%223%5E%28%282%2Bq%29-%28q%2B5%29%29

Simplify the exponents:

3%5E%28q%2B3-q-5%29%22%22-%22%223%5E%282%2Bq-q-5%29

3%5E%28-2%29%22%22-%22%223%5E%28-3%29

Get rid of the negative exponents by putting them in the
denominators with positive exponents:

1%2F3%5E2%22%22-%22%221%2F3%5E3

1%2F9%22%22-%22%221%2F27

Get an LCD of 27

%281%2A3%29%2F%289%2A3%29%22%22-%22%221%2F27

3%2F27%22%22-%22%221%2F27

2%2F27

Edwin