Question

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

Short answer

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

Step-by-step solution

Given Information

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

Find the LCD of denominators.

Factor the denominators.

$10x^{2}y=2\times 5\times x\times x\times y$

$15x{y}^2=3\times 5\times x\times y\times y$

LCD$=2\times 3\times 5\times x\times x\times y\times y$

LCD$=30x^2{y}^2$

Rewrite each fraction as an equivalent fraction with the LCD.

$=\frac{7·3y}{10x^{2}y·3y}+\frac{4·2x}{15x{y}^2·2x}$

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

Add

Take common denominator.

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