Question

In the following exercises, perform indicated operations.

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

Short answer

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

Step-by-step solution

Step 1. Given Information

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

Step 2. Express with common denominator   

• Factor the denominators of the given expression.

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

• The LCD of the terms of obtained expression is $a^2(b+2)(b-2)$.
• Multiply the numerator and denominator of first term by $(b+2)$and second term by $a^2$.

role="math" localid="1645428256449" $\frac{5b(b+2)}{a^2(b-2)(b+2)}+\frac{2b\left(a^2\right)}{(b+2)(b-2)\left(a^2\right)}=\frac{5b^2+10b}{a^2(b-2)(b+2)}+\frac{2a^{2}b}{a^2(b+2)(b-2)}$

Step 3. Simplify

• As the denominator is the same for both the terms, perform addition in the numerator and place it over the common denominator.

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

• So, the resultant expression is $\frac{b(5b+10+2a^2)}{a^2(b-2)(b+2)}$.