Question

Simplify the expression$\frac{\frac{m+n}{5}}{\frac{m^2+n^2}{5}}$

Short answer

The simplified value of expression is$\frac{m+n}{m^2+n^2}$

Step-by-step solution

Step 1. Write down the given expression.

The given expression is$\frac{\frac{m+n}{5}}{\frac{m^2+n^2}{5}}$

Step 2. Simplify the expression.

The given expression $\frac{\frac{m+n}{5}}{\frac{m^2+n^2}{5}}$is simplified as:

$\begin{array}{c}\frac{\frac{m+n}{5}}{\frac{m^2+n^2}{5}}=\frac{m+n}{5}\times \frac{5}{m^2+n^2}\\ =\frac{m+n}{m^2+n^2}\end{array}$

Step 3. Conclusion.

The simplified value of expression is$\frac{m+n}{m^2+n^2}$