Question Simplify $\frac{x^{4}+7 x^{3}-10 x^{2}-63 x+9}{x^{2}-9}$ where $x^{2} \neq 9$ using long or synthetic division.

Studdy Solution
Since the remainder $-1215$ is a constant, it cannot be simplified further when divided by $x^{2}-9$. Therefore, the simplified form of the original rational expression is:
$$x^{2}+7x-10 + \frac{-1215}{x^{2}-9}$$
This is the final simplified form of the given rational expression.