Question

question #8 multiply the rational expressions. write the product in simplest form. $\frac{10x}{5x - 15}cdot\frac{x - 3}{8}$ $\frac{2x}{5}$ $\frac{x}{2}$ $\frac{5x}{8}$ $\frac{x}{4}$

Explanation:

Step1: Factor the denominator

Factor $5x - 15$ as $5(x - 3)$. So the expression becomes $\frac{10x}{5(x - 3)}\cdot\frac{x - 3}{8}$.

Step2: Multiply the numerators and denominators

Multiply numerators $10x\cdot(x - 3)$ and denominators $5(x - 3)\cdot8$. We get $\frac{10x(x - 3)}{40(x - 3)}$.

Step3: Simplify the fraction

Cancel out the common factor $(x - 3)$ in the numerator and denominator. Also, simplify $\frac{10x}{40}$ by dividing both numerator and denominator by 10. We have $\frac{x}{4}$.

Answer:

$\frac{x}{4}$