Question

In the following exercises, perform the indicated operations .

$\frac{5}{x^{2}y}+\frac{7}{20x{y}^3}$

Short answer

Simplified expression is$\frac{100y^2+7x}{20x^2{y}^3}$

Step-by-step solution

Step 1. Given expression 

$\frac{5}{x^{2}y}+\frac{7}{20x{y}^3}$

Step 2. Find LCD       

Denominator of the first fraction is $x^{2}y$

Denominator of the second fraction $20x{y}^3$

Here is common to both denominators

So LCD is $20x^2{y}^3$

Step 3. Rewrite each rational expression as  an equivalent rational expression with the LCD    

$\frac{5·20y^2}{20x^2{y}^3}+\frac{7x}{20x^2{y}^3}$

Step 4. Simplify and  Add numerators

$\frac{100y^2+7x}{20x^2{y}^3}$