Solve x-y/a+b/frac{x^2-y^2{b^2-a^2}}

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

Evaluate

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

Short Solution Steps

Divide \frac{x-y}{a+b} by \frac{x^{2}-y^{2}}{b^{2}-a^{2}} by multiplying \frac{x-y}{a+b} by the reciprocal of \frac{x^{2}-y^{2}}{b^{2}-a^{2}}.

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

Factor the expressions that are not already factored.

$$\frac{\left(a+b\right)\left(b-a\right)\left(x-y\right)}{\left(a+b\right)\left(x+y\right)\left(x-y\right)}$$

Cancel out \left(a+b\right)\left(x-y\right) in both numerator and denominator.

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

Expand

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

Short Solution Steps

Divide \frac{x-y}{a+b} by \frac{x^{2}-y^{2}}{b^{2}-a^{2}} by multiplying \frac{x-y}{a+b} by the reciprocal of \frac{x^{2}-y^{2}}{b^{2}-a^{2}}.

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

Factor the expressions that are not already factored.

$$\frac{\left(a+b\right)\left(b-a\right)\left(x-y\right)}{\left(a+b\right)\left(x+y\right)\left(x-y\right)}$$

Cancel out \left(a+b\right)\left(x-y\right) in both numerator and denominator.

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