1. Solve really fast anyone?

$(a^2n-a^n-6)/(a^n+8)$

Divide.

2. Originally Posted by A Beautiful Mind
$(a^2n-a^n-6)/(a^n+8)$

Divide.
Synthetic division:

-8 | 1 -1 -6
__| 0 +8 +56
___1__7__50

1*a^n + 7 + 50/(a^n+8)
= a^n + 7 + 50/(a^n+8)

You can do it with long division as well.

idk the easy way for formatting

3. Hello, A Beautiful Mind!

Is there a second typo?
The problem would make more sense . . .

Divide: . $\frac{a^{2n}-a^n-6}{a^{{\color{red}3}n}+8}$

Factor: . $\frac{(a^n+2)(a^n-3)}{(a^n+2)(a^{2n}-2a^n + 4)}$

Reduce: . $\frac{a^n - 3}{a^{2n} - 2a^n + 4}$

4. Second typo?

I only edited my first post to say divide, lol.

$I found that the answer is: a^n - 9 + 66/a^n+8...just don't know how to get there.$

5. Yes, the first typo was the exponent "2n" . . .

You have: . $(a^{{\color{red}2n}} - a^n - 6) \div (a^n + 8)$

Long division:

. . $\begin{array}{cccccccc}
&&&& a^n & - & 9 \\
& & -- & -- & -- & --& -- \\
a^n + 8 & ) & a^{2n} & - & a^n & - & 6 \\
& & a^{2n} & + & 8a^n \\
& & -- & -- & -- \\
& & & - & 9a^n & - & 6 \\
& & & - & 9a^n & - & 72 \\
& & & -- & -- & -- & -- \\
& & & & & & 66 \end{array}$

Answer: . $a^n - 9 + \frac{66}{a^n+8}$