For the given functions $f(x)$ and $g(x)$, find $f(x) \cdot g(x)$.
-$f(x)=\frac{8}{(x-8)}, g(x)=\frac{x^{2}-4 x-32}{(x+4)^{2}}$

A) $\frac{8(x-8)}{x+4}$

B) $8(x+4)$

C) $\frac{8}{x+4}$

D) $\frac{8}{x-8}$

Question

For the given functions $f(x)$ and $g(x)$, find $f(x) \cdot g(x)$.
-$f(x)=\frac{8}{(x-8)}, g(x)=\frac{x^{2}-4 x-32}{(x+4)^{2}}$

A) $\frac{8(x-8)}{x+4}$

B) $8(x+4)$

C) $\frac{8}{x+4}$

D) $\frac{8}{x-8}$

Quizplus · Accepted Answer

To find $f(x) \cdot g(x)$, we multiply $f(x)=\frac{8}{(x-8)}$ by $g(x)=\frac{x^{2}-4 x-32}{(x+4)^{2}}$. Simplifying $g(x)$ by factoring the numerator as $(x-8)(x+4)$, we get $g(x)=\frac{(x-8)(x+4)}{(x+4)^{2}}$. Multiplying $f(x)$ and $g(x)$ gives $\frac{8}{(x-8)} \cdot \frac{(x-8)(x+4)}{(x+4)^{2}}$, which simplifies to $\frac{8}{x+4}$ after canceling out $(x-8)$.

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