Solve frac{x^{2}}{x^{2}-y^{2}}+frac{y^{2}}{x^2-y^2}-2xy/x^2-y^2

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

Evaluate

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

Short Solution Steps

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

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

Since \frac{x^{2}+y^{2}}{x^{2}-y^{2}} and \frac{2xy}{x^{2}-y^{2}} have the same denominator, subtract them by subtracting their numerators.

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

Factor the expressions that are not already factored in \frac{x^{2}+y^{2}-2xy}{x^{2}-y^{2}}.

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

Cancel out x-y in both numerator and denominator.

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

Factor

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