Question

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

The 2n is in exponent form.

Answer 1

@AJ01

Answer 2

The numerator can be factored as a quadratic:
\[\frac{a^{2n}-a^n-6}{a^n+8}=\frac{(a^n-3)(a^n+2)}{a^n+8}\]
By any chance, did you mean to write \(a^{3n}\) in the denominator?

Answer 3

There is no a^3n.

Answer 4

I only ask because you could have factored that as a sum of cubes. What exactly are you supposed to do here?

Answer 5

Divide?

Answer 6

Alright, let's try synthetic division. First, let's replace \(a^n\) with something simpler, like \(x\):
\[\frac{a^{2n}-a^n-6}{a^n+8}=\frac{x^2-x-6}{x+8}\]

which means the quotient is
\[x-9+\frac{78}{x+8}=a^n-9+\frac{78}{a^n+8}\]