Question

question #1 perform the indicated operation. write the answer in simplest form. $\frac{x + 1}{x^{2}+x}cdot\frac{x^{2}-5x}{x^{2}+14x + 48}$
-5
o $\frac{-5}{(x + 8)(x + 6)}$
o $\frac{5}{(x + 8)(x + 6)}$
o $\frac{x - 5}{(x + 8)(x + 6)}$
o $\frac{x + 5}{(x + 8)(x + 6)}$

Explanation:

Step1: Factor the expressions

Factor $x^{2}+x=x(x + 1)$, $x^{2}-5x=x(x - 5)$ and $x^{2}+14x + 48=(x + 6)(x+8)$. So the original expression $\frac{x + 1}{x^{2}+x}\cdot\frac{x^{2}-5x}{x^{2}+14x + 48}$ becomes $\frac{x + 1}{x(x + 1)}\cdot\frac{x(x - 5)}{(x + 6)(x + 8)}$.

Step2: Cancel out common factors

Cancel out the common factors $x+1$ and $x$. We get $\frac{1}{1}\cdot\frac{x - 5}{(x + 6)(x + 8)}=\frac{x - 5}{(x + 6)(x + 8)}$.

Answer:

$\frac{x - 5}{(x + 8)(x + 6)}$