Solve frac{x^{4}-y^{4}}{x^2-2xy+y^2}divx^2+y^2/y-x

$$\frac { x ^ { 4 } - y ^ { 4 } } { x ^ { 2 } - 2 x y + y ^ { 2 } } \div \frac { x ^ { 2 } + y ^ { 2 } } { y - x }$$

Evaluate

$$-\left(x+y\right)$$

Short Solution Steps

Divide \frac{x^{4}-y^{4}}{x^{2}-2xy+y^{2}} by \frac{x^{2}+y^{2}}{y-x} by multiplying \frac{x^{4}-y^{4}}{x^{2}-2xy+y^{2}} by the reciprocal of \frac{x^{2}+y^{2}}{y-x}.

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

Factor the expressions that are not already factored.

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

Cancel out \left(x-y\right)\left(x^{2}+y^{2}\right) in both numerator and denominator.

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

Expand the expression.

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

Factor the expressions that are not already factored.

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

Cancel out x-y in both numerator and denominator.

$$-x-y$$

Expand

$$-x-y$$

Short Solution Steps

Divide \frac{x^{4}-y^{4}}{x^{2}-2xy+y^{2}} by \frac{x^{2}+y^{2}}{y-x} by multiplying \frac{x^{4}-y^{4}}{x^{2}-2xy+y^{2}} by the reciprocal of \frac{x^{2}+y^{2}}{y-x}.

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

Factor the expressions that are not already factored.

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

Cancel out \left(x-y\right)\left(x^{2}+y^{2}\right) in both numerator and denominator.

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

Expand the expression.

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

Factor the expressions that are not already factored.

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

Cancel out x-y in both numerator and denominator.

$$-x-y$$