Question

In the following exercises, perform indicated operations.

$\frac{1}{12a^3{b}^2}+\frac{5}{9a^2{b}^3}$

Short answer

The resultant expression is$\frac{3b+20a}{36a^3{b}^3}$.

Step-by-step solution

Step 1. Given Information

The given expression is$\frac{1}{12a^3{b}^2}+\frac{5}{9a^2{b}^3}$

Step 2. Express with common denominator 

• Factor the denominators of the given expression.

$\frac{1}{4·3·a·a·a·b·b}+\frac{5}{3·3·a·a·b·b·b}$

• The LCD of the terms of given expression is $36a^3{b}^3$.
• Multiply the numerator and denominator of first term by $3b$and second term by $4a$.

role="math" localid="1645164948338" $\frac{1\left(3b\right)}{12a^3{b}^2\left(3b\right)}+\frac{5\left(4a\right)}{9a^2{b}^3\left(4a\right)}=\frac{3b}{36a^3{b}^3}+\frac{20a}{36a^3{b}^3}$

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.

$\frac{3b+20a}{36a^3{b}^3}$

• So, the resultant expression is $\frac{3b+20a}{36a^3{b}^3}$.