Question

question #7 perform the indicated operation. write the answer in simplest form. $\frac{5x - 1}{5x^{2}-41x + 8}cdot\frac{6x^{2}+6x}{6x^{2}-24x}$ o $\frac{x - 1}{(x - 8)(x - 4)}$ o $\frac{x - 1}{(x + 8)(x + 4)}$ o $\frac{x + 1}{(x + 8)(x + 4)}$ o $\frac{x + 1}{(x - 8)(x - 4)}$

Explanation:

Step1: Factor the polynomials

Factor $5x^{2}-41x + 8=(5x - 1)(x - 8)$; factor $6x^{2}+6x = 6x(x + 1)$; factor $6x^{2}-24x=6x(x - 4)$.

Step2: Rewrite the expression

The original expression $\frac{5x - 1}{5x^{2}-41x + 8}\cdot\frac{6x^{2}+6x}{6x^{2}-24x}$ becomes $\frac{5x - 1}{(5x - 1)(x - 8)}\cdot\frac{6x(x + 1)}{6x(x - 4)}$.

Step3: Cancel out common factors

Cancel out the common factors $5x - 1$, $6x$. We get $\frac{x + 1}{(x - 8)(x - 4)}$.

Answer:

$\frac{x + 1}{(x - 8)(x - 4)}$ (the last option)