select the correct answer. if no denominator equals zero, which expression is equivalent to $\frac{15}{x…

select the correct answer. if no denominator equals zero, which expression is equivalent to $\frac{15}{x - 6}+\frac{7}{x + 6}$?\na. $\frac{22x + 132}{x^{2}-36}$\nb. $\frac{22x - 48}{x^{2}-36}$\nc. $\frac{22}{x^{2}-36}$\nd. $\frac{22x + 48}{x^{2}-36}$

select the correct answer. if no denominator equals zero, which expression is equivalent to $\frac{15}{x - 6}+\frac{7}{x + 6}$?\na. $\frac{22x + 132}{x^{2}-36}$\nb. $\frac{22x - 48}{x^{2}-36}$\nc. $\frac{22}{x^{2}-36}$\nd. $\frac{22x + 48}{x^{2}-36}$

Answer

Explanation:

Step1: Find common denominator

The common denominator of $\frac{15}{x - 6}$ and $\frac{7}{x + 6}$ is $(x - 6)(x + 6)=x^{2}-36$.

Step2: Rewrite fractions with common denominator

$\frac{15}{x - 6}\times\frac{x + 6}{x + 6}=\frac{15(x + 6)}{x^{2}-36}=\frac{15x+90}{x^{2}-36}$; $\frac{7}{x + 6}\times\frac{x - 6}{x - 6}=\frac{7(x - 6)}{x^{2}-36}=\frac{7x-42}{x^{2}-36}$.

Step3: Add the fractions

$\frac{15x + 90}{x^{2}-36}+\frac{7x-42}{x^{2}-36}=\frac{(15x + 90)+(7x-42)}{x^{2}-36}=\frac{15x+7x + 90-42}{x^{2}-36}=\frac{22x + 48}{x^{2}-36}$.

Answer:

D. $\frac{22x + 48}{x^{2}-36}$