Question

question #4 which of the following would be the second step in writing the rational expression in simplest form? $\frac{4x + 8}{x + 1}cdot\frac{x^{2}-2x - 3}{3x^{2}-24x + 45}$ $\bigcirc\frac{4(x + 2)}{x + 1}cdot\frac{(x - 3)(x + 1)}{3(x - 5)(x - 3)}$ $\bigcirc\frac{4(x + 2)(x - 3)}{3(x - 5)(x - 3)}$ $\bigcirc\frac{4(x + 2)}{x + 1}cdot\frac{x^{2}-2x - 3}{3(x^{2}-8x + 15)}$ $\bigcirc\frac{4(x + 2)}{3(x - 5)}$ question #5 perform the indicated operation. write the answer in simplest form. $\frac{p^{2}-9p + 18}{p^{2}-11p + 30}cdot\frac{p - 5}{p^{2}+2p - 15}$

Explanation:

Step1: Factor the expressions

Factor $4x + 8$ to $4(x + 2)$, factor $x^{2}-2x - 3$ to $(x - 3)(x+1)$, factor $3x^{2}-24x + 45$ to $3(x^{2}-8x + 15)$ and further to $3(x - 3)(x - 5)$. So the original expression $\frac{4x + 8}{x + 1}\cdot\frac{x^{2}-2x - 3}{3x^{2}-24x + 45}$ becomes $\frac{4(x + 2)}{x + 1}\cdot\frac{(x - 3)(x + 1)}{3(x - 5)(x - 3)}$.

Step2: Cancel out common factors

Cancel out the common factors $(x + 1)$ and $(x - 3)$ in the numerator and denominator. We get $\frac{4(x + 2)}{3(x - 5)}$.

Answer:

$\frac{4(x + 2)}{3(x - 5)}$ (corresponding to the last - option in the multiple - choice list for Question #4)