Solve 3/2x-y-2/x+y=

$$\frac { 3 } { 2 x - y } - \frac { 2 } { x + y } =$$

Evaluate

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2x-y and x+y is \left(x+y\right)\left(2x-y\right). Multiply \frac{3}{2x-y} times \frac{x+y}{x+y}. Multiply \frac{2}{x+y} times \frac{2x-y}{2x-y}.

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

Since \frac{3\left(x+y\right)}{\left(x+y\right)\left(2x-y\right)} and \frac{2\left(2x-y\right)}{\left(x+y\right)\left(2x-y\right)} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in 3\left(x+y\right)-2\left(2x-y\right).

$$\frac{3x+3y-4x+2y}{\left(x+y\right)\left(2x-y\right)}$$

Combine like terms in 3x+3y-4x+2y.

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

Expand \left(x+y\right)\left(2x-y\right).

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

Differentiate w.r.t. x

$$\frac{2\left(x^{2}-10xy-2y^{2}\right)}{\left(\left(2x-y\right)\left(x+y\right)\right)^{2}}$$