Solve 2x/x-y+7x^2/x^2-y^2

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

Evaluate

$$\frac{x\left(9x+2y\right)}{x^{2}-y^{2}}$$

Short Solution Steps

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

$$\frac{2x}{x-y}+\frac{7x^{2}}{\left(x+y\right)\left(x-y\right)}$$

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

$$\frac{2x\left(x+y\right)}{\left(x+y\right)\left(x-y\right)}+\frac{7x^{2}}{\left(x+y\right)\left(x-y\right)}$$

Since \frac{2x\left(x+y\right)}{\left(x+y\right)\left(x-y\right)} and \frac{7x^{2}}{\left(x+y\right)\left(x-y\right)} have the same denominator, add them by adding their numerators.

$$\frac{2x\left(x+y\right)+7x^{2}}{\left(x+y\right)\left(x-y\right)}$$

Do the multiplications in 2x\left(x+y\right)+7x^{2}.

$$\frac{2x^{2}+2xy+7x^{2}}{\left(x+y\right)\left(x-y\right)}$$

Combine like terms in 2x^{2}+2xy+7x^{2}.

$$\frac{9x^{2}+2xy}{\left(x+y\right)\left(x-y\right)}$$

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

$$\frac{9x^{2}+2xy}{x^{2}-y^{2}}$$

Factor

$$\frac{x\left(9x+2y\right)}{x^{2}-y^{2}}$$