Question

question #14
perform the indicated operation for the given rational expressions:
$\frac{4}{v - 6}+\frac{2}{5v - 6}$. write the answer in simplest form.
$\frac{22v - 36}{(v - 6)(5v - 6)}$
$\frac{6}{(v - 6)(5v - 6)}$
$\frac{8}{(v - 6)(5v - 6)}$
$\frac{16v}{(v - 1)(v + 1)}$

Explanation:

Step1: Find common denominator

The common denominator of $\frac{4}{v - 6}$ and $\frac{2}{5v - 6}$ is $(v - 6)(5v - 6)$.

Step2: Rewrite fractions with common denominator

$\frac{4}{v - 6}\times\frac{5v - 6}{5v - 6}=\frac{4(5v - 6)}{(v - 6)(5v - 6)}=\frac{20v-24}{(v - 6)(5v - 6)}$ and $\frac{2}{5v - 6}\times\frac{v - 6}{v - 6}=\frac{2(v - 6)}{(v - 6)(5v - 6)}=\frac{2v-12}{(v - 6)(5v - 6)}$.

Step3: Add the fractions

$\frac{20v - 24}{(v - 6)(5v - 6)}+\frac{2v - 12}{(v - 6)(5v - 6)}=\frac{(20v - 24)+(2v - 12)}{(v - 6)(5v - 6)}=\frac{20v+2v-24 - 12}{(v - 6)(5v - 6)}=\frac{22v-36}{(v - 6)(5v - 6)}$

Answer:

$\frac{22v - 36}{(v - 6)(5v - 6)}$