For the given functions $f(x)$ and $g(x)$, find $f(x) \cdot g(x)$.
-$f(x)=\frac{x^{2}+5 x+6}{x^{2}+8 x+12}, g(x)=\frac{x^{2}-5 x-6}{x^{2}+4 x+3}$

A) $\frac{x-6}{x+6}$

B) -1

C) $\frac{x+6}{x-6}$

D) 1

Question

For the given functions $f(x)$ and $g(x)$, find $f(x) \cdot g(x)$.
-$f(x)=\frac{x^{2}+5 x+6}{x^{2}+8 x+12}, g(x)=\frac{x^{2}-5 x-6}{x^{2}+4 x+3}$

A) $\frac{x-6}{x+6}$

B) -1

C) $\frac{x+6}{x-6}$

D) 1

Quizplus · Accepted Answer

To find $f(x) \cdot g(x)$, first factorize the numerators and denominators of $f(x)$ and $g(x)$:$$f(x)=\frac{(x+2)(x+3)}{(x+2)(x+6)}$$$$g(x)=\frac{(x-6)(x+1)}{(x+1)(x+3)}$$Multiplying $f(x)$ and $g(x)$ gives:$$f(x) \cdot g(x) = \frac{(x+2)(x+3)}{(x+2)(x+6)} \cdot \frac{(x-6)(x+1)}{(x+1)(x+3)}$$Simplifying by canceling out common factors $(x+2), (x+3),$ and $(x+1)$ gives:$$f(x) \cdot g(x) = \frac{x-6}{x+6}$$

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For the Given Functions $f(x)$ And $g(x)$ , Find $f(x) \cdot g(x)$
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