Question

In the following exercises, perform indicated operations.

$\frac{7}{10x^{2}y}+\frac{4}{15x{y}^2}$

Short answer

The resultant expression is$\frac{21y+8x}{30x^2{y}^2}$.

Step-by-step solution

Step 1. Given Information

The given expression is$\frac{7}{10x^{2}y}+\frac{4}{15x{y}^2}$.

Step 2. Express with common denominator

• Factor the denominators of the given expression.

$\frac{7}{2·5·x·x·y}+\frac{4}{3·5·x·y·y}$

• The LCD of the terms of given expression is $30x^2{y}^2$.
• Multiply the numerator and denominator of first term by $3y$and second term by $2x$.

role="math" localid="1645163338497" $\frac{7\left(3y\right)}{10x^{2}y\left(3y\right)}+\frac{4\left(2x\right)}{15x{y}^2\left(2x\right)}=\frac{21y}{30x^2{y}^2}+\frac{8x}{30x^2{y}^2}$

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.

$\frac{21y+8x}{30x^2{y}^2}$

• So, the resultant expression is $\frac{21y+8x}{30x^2{y}^2}$.