We are asked to add the two fractions $\frac{20}{7xy}$ and $\frac{5}{7y^2}$ and simplify the result.

1. Problem Description

We are asked to add the two fractions $\frac{20}{7xy}$ and $\frac{5}{7y^2}$ and simplify the result.

2. Solution Steps

To add the two fractions, we need to find a common denominator. The denominators are $7xy$ and $7y^2$.

The least common multiple of $7xy$ and $7y^2$ is $7xy^2$.

We rewrite each fraction with the common denominator of $7xy^2$.

$\frac{20}{7xy} = \frac{20}{7xy} \cdot \frac{y}{y} = \frac{20y}{7xy^2}$.

$\frac{5}{7y^2} = \frac{5}{7y^2} \cdot \frac{x}{x} = \frac{5x}{7xy^2}$.

Now we can add the fractions:

$\frac{20y}{7xy^2} + \frac{5x}{7xy^2} = \frac{20y + 5x}{7xy^2}$.

We can factor a $5$ out of the numerator:

$\frac{20y + 5x}{7xy^2} = \frac{5(4y + x)}{7xy^2}$.

3. Final Answer

$\frac{5(x+4y)}{7xy^2}$