Hi, in my math textbook I have three question which the textbook does not teach you how to simplify please help. I don't just want the answer I want to know how to get the answer again if I receive a similar question.

These are the three questions. The correct answers are below each question question

Simplify...

131. (2^(n+2) + 12) / (5 * 2^n + 15)
4/5
132. (2^(2n+3) - (2n)^2) / 2^n
7 * (2^n)
133. (3^(n+1) + 9) / (3^(n-1) + 1)
9

2. $\displaystyle 2^{n+2}+12=4(2^n+3)$
and
$\displaystyle 5\cdot 2^{n}+15=5(2^n+3)$

3. Thankyou for your quick response.
But I still need help with the other 2 questions if you could
I must be doing something wrong :S

4. Hello, stripe501!

$\displaystyle 132.\;\;\dfrac{2^{2n+3} - (2n)^2}{2^n}$

$\displaystyle \text{Answer: }\:7\cdot2^n$

We have: .$\displaystyle \displaystyle \frac{2^{2n+3} - 2^{2n}}{2^n} \;=\;\frac{2^{2n}(2^3-1)}{2^n} \;=\;\frac{2^{2n}\cdot 7}{2^n} \;=\;7\cdot2^n$

$\displaystyle 133.\;\;\dfrac{3^{n+1} + 9}{3^{n-1} + 1}$

$\displaystyle \text{Answer: }\:9$

$\displaystyle \displaystyle \text{We have: }\;\frac{3^{n+1} + 3^2}{3^{n-1}+1} \;=\;\frac{3^2(3^{n-1}+1)}{3^{n-1}+1} \;=\;3^2 \;=\;9$

5. Both of you thanks for your help. Much appreciated

6. I under stand everything accept for how you get from (2^(2n) * 7) / 2n
to 7 * 2^n
7. $\displaystyle \dfrac{2^{2n} \cdot 7}{2^n} = \dfrac{(2^n)^2\cdot 7}{2^n} = \dfrac{2^n \cdot 2^n \cdot 7}{2^n} = 2^n \cdot 7$