Solve 2m+2n/5m+5n/x-y

$$\frac { 2 m + 2 n / 5 m + 5 n } { x - y }$$

Evaluate

$$\frac{2mn+10m+25n}{5\left(x-y\right)}$$

Short Solution Steps

Express \frac{2n}{5}m as a single fraction.

$$\frac{2m+\frac{2nm}{5}+5n}{x-y}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 2m+5n times \frac{5}{5}.

$$\frac{\frac{5\left(2m+5n\right)}{5}+\frac{2nm}{5}}{x-y}$$

Since \frac{5\left(2m+5n\right)}{5} and \frac{2nm}{5} have the same denominator, add them by adding their numerators.

$$\frac{\frac{5\left(2m+5n\right)+2nm}{5}}{x-y}$$

Do the multiplications in 5\left(2m+5n\right)+2nm.

$$\frac{\frac{10m+25n+2nm}{5}}{x-y}$$

Express \frac{\frac{10m+25n+2nm}{5}}{x-y} as a single fraction.

$$\frac{10m+25n+2nm}{5\left(x-y\right)}$$

Use the distributive property to multiply 5 by x-y.

$$\frac{10m+25n+2nm}{5x-5y}$$

Expand

$$\frac{2mn+10m+25n}{5\left(x-y\right)}$$

Short Solution Steps

Express \frac{2n}{5}m as a single fraction.

$$\frac{2m+\frac{2nm}{5}+5n}{x-y}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 2m+5n times \frac{5}{5}.

$$\frac{\frac{5\left(2m+5n\right)}{5}+\frac{2nm}{5}}{x-y}$$

Since \frac{5\left(2m+5n\right)}{5} and \frac{2nm}{5} have the same denominator, add them by adding their numerators.

$$\frac{\frac{5\left(2m+5n\right)+2nm}{5}}{x-y}$$

Do the multiplications in 5\left(2m+5n\right)+2nm.

$$\frac{\frac{10m+25n+2nm}{5}}{x-y}$$

Express \frac{\frac{10m+25n+2nm}{5}}{x-y} as a single fraction.

$$\frac{10m+25n+2nm}{5\left(x-y\right)}$$

Use the distributive property to multiply 5 by x-y.

$$\frac{10m+25n+2nm}{5x-5y}$$