Question

Add$\frac{5b}{a^{2}b-2a^2}+\frac{2b}{b^2-4}$.

Short answer

The sum is$\frac{b(5b+10+2a^2)}{a^2(b+2)(b-2)}$.

Step-by-step solution

Given Information 

The Given expression is$\frac{5b}{a^{2}b-2a^2}+\frac{2b}{b^2-4}$.

Find the LCD of denominators. 

Factor the denominators.

$a^{2}b-2a^2=a^2(b-2)$

$b^2-4=(b+2)(b-2)$

LCD$=a^2(b+2)(b-2)$

Rewrite each fraction as an equivalent fraction with the LCD. 

$=\frac{5b(b+2)}{a^2(b+2)(b-2)}+\frac{2b\left(a^2\right)}{a^2(b+2)(b-2)}$

Simplify numerator.

$=\frac{5b^2+10b}{a^2(b+2)(b-2)}+\frac{2a^{2}b}{a^2(b+2)(b-2)}$

Add

Take common denominator.

$=\frac{5b^2+10b+2a^{2}b}{a^2(b+2)(b-2)}$

Simplify numerator.

$=\frac{b(5b+10+2a^2)}{a^2(b+2)(b-2)}$