Multiply and, if possible, simplify.
-$\frac{x^{4}-81}{x^{4}-1} \cdot \frac{x^{2}+1}{x^{2}+9}$
A) $\frac{(x+3)(x-3)}{(x+1)(x-1)}$
B) $\frac{x+3}{x-1}$
C) $\frac{x-3}{x+1}$
D) $\frac{x-3}{x-1}$

Question

Quizplus · Accepted Answer

The given expression can be simplified by factoring the polynomials. The numerator $x^4 - 81$ can be factored as $(x^2 + 9)(x^2 - 9)$, and $x^2 - 9$ can further be factored as $(x + 3)(x - 3)$. The denominator $x^4 - 1$ can be factored as $(x^2 + 1)(x^2 - 1)$, and $x^2 - 1$ can further be factored as $(x + 1)(x - 1)$. After canceling out the common terms $(x^2 + 1)$, the simplified expression is $\frac{(x+3)(x-3)}{(x+1)(x-1)}$.