Solve (2x+y/2x-y)+(5x-5y/2x-y)+(y-x/2x-y)

$$( \frac { 2 x + y } { 2 x - y } ) + ( \frac { 5 x - 5 y } { 2 x - y } ) + ( \frac { y - x } { 2 x - y } )$$

Evaluate

$$3$$

Short Solution Steps

Since \frac{2x+y}{2x-y} and \frac{5x-5y}{2x-y} have the same denominator, add them by adding their numerators.

$$\frac{2x+y+5x-5y}{2x-y}+\frac{y-x}{2x-y}$$

Combine like terms in 2x+y+5x-5y.

$$\frac{7x-4y}{2x-y}+\frac{y-x}{2x-y}$$

Since \frac{7x-4y}{2x-y} and \frac{y-x}{2x-y} have the same denominator, add them by adding their numerators.

$$\frac{7x-4y+y-x}{2x-y}$$

Combine like terms in 7x-4y+y-x.

$$\frac{6x-3y}{2x-y}$$

Factor the expressions that are not already factored in \frac{6x-3y}{2x-y}.

$$\frac{3\left(2x-y\right)}{2x-y}$$

Cancel out 2x-y in both numerator and denominator.

$$3$$

Factor

$$3$$