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

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

Evaluate

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

Short Solution Steps

Factor y^{2}-x^{2}.

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

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

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

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

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

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

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

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

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

Differentiate w.r.t. x

$$\frac{3x^{2}+6xy+4x+3y^{2}}{\left(y^{2}-x^{2}\right)^{2}}$$