Question

question #4
perform the indicated operation for the given rational expressions:
$\frac{6}{x - 4}+\frac{6}{x + 3}$. write the answer in simplest form.
$\frac{12x - 6}{(x - 4)(x + 3)}$
$\frac{12}{2x - 1}$
$\frac{12}{(x - 4)(x + 3)}$
$\frac{12x + 6}{(x - 4)(x + 3)}$

Explanation:

Step1: Find common denominator

The common denominator of $\frac{6}{x - 4}$ and $\frac{6}{x + 3}$ is $(x - 4)(x + 3)$.

Step2: Rewrite fractions with common denominator

$\frac{6}{x - 4}\times\frac{x + 3}{x + 3}=\frac{6(x + 3)}{(x - 4)(x + 3)}$ and $\frac{6}{x + 3}\times\frac{x - 4}{x - 4}=\frac{6(x - 4)}{(x - 4)(x + 3)}$.

Step3: Add the fractions

$\frac{6(x + 3)}{(x - 4)(x + 3)}+\frac{6(x - 4)}{(x - 4)(x + 3)}=\frac{6(x + 3)+6(x - 4)}{(x - 4)(x + 3)}$.

Step4: Expand numerator

$6(x + 3)+6(x - 4)=6x+18 + 6x-24=12x - 6$.
So the result is $\frac{12x - 6}{(x - 4)(x + 3)}$.

Answer:

$\frac{12x - 6}{(x - 4)(x + 3)}$