1. ## Index Laws

Hello

Here's the problem I need a hand with, I need to simplify it:

(3^2n + 5x3^n + 6)/(3^n + 3)

Thanks in advance, all help is really appreciated

2. Recall that: $\displaystyle a^{bc} = \left(a^b\right)^c$

$\displaystyle \frac{3^{2n} + 5\cdot 3^n + 6}{3^n + 3} = \frac{\left({\color{blue}3^n}\right)^2 + 5\cdot {\color{blue}3^n} + 6}{{\color{blue}3^n} + 6}$

Now it might be hard to see but the numerator essentially resembles a quadratic that you can factor. To see, let $\displaystyle \color{blue} x = 3^n$.

This yields: $\displaystyle \frac{{\color{blue}n}^2 + 5{\color{blue}n} + 6}{{\color{blue}n} + 6}$

Can you do it now?