Question

question #6 simplify the rational expression $\frac{6x^{2}-15x}{x^{2}-5x}$
$\frac{3}{x}$
$5x^{2}-10x$
$\frac{3(2x - 5)}{x - 5}$
$\frac{2x - 5}{x - 5}$

Explanation:

Step1: Factor the numerator and denominator

Factor out the greatest - common factor from the numerator $6x^{2}-15x = 3x(2x - 5)$ and from the denominator $x^{2}-5x=x(x - 5)$. So the expression becomes $\frac{3x(2x - 5)}{x(x - 5)}$.

Step2: Cancel out the common factor

Cancel out the common non - zero factor $x$ (assuming $x
eq0$) from the numerator and the denominator. We get $\frac{3(2x - 5)}{x - 5}$.

Answer:

C. $\frac{3(2x - 5)}{x - 5}$