Solve 4x/x^2-y^2-6/y-x

$$\frac { 4 x } { x ^ { 2 } - y ^ { 2 } } - \frac { 6 } { y - x }$$

Evaluate

$$-\frac{2\left(5x+3y\right)}{y^{2}-x^{2}}$$

Short Solution Steps

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

$$\frac{4x}{\left(x+y\right)\left(x-y\right)}-\frac{6}{y-x}$$

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{4x}{\left(x+y\right)\left(x-y\right)} times \frac{-1}{-1}. Multiply \frac{6}{y-x} times \frac{x+y}{x+y}.

$$\frac{-4x}{\left(x+y\right)\left(-x+y\right)}-\frac{6\left(x+y\right)}{\left(x+y\right)\left(-x+y\right)}$$

Since \frac{-4x}{\left(x+y\right)\left(-x+y\right)} and \frac{6\left(x+y\right)}{\left(x+y\right)\left(-x+y\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-4x-6\left(x+y\right)}{\left(x+y\right)\left(-x+y\right)}$$

Do the multiplications in -4x-6\left(x+y\right).

$$\frac{-4x-6x-6y}{\left(x+y\right)\left(-x+y\right)}$$

Combine like terms in -4x-6x-6y.

$$\frac{-10x-6y}{\left(x+y\right)\left(-x+y\right)}$$

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

$$\frac{-10x-6y}{-x^{2}+y^{2}}$$

Factor

$$-\frac{2\left(5x+3y\right)}{y^{2}-x^{2}}$$