Solve frac{x^{3}y^{2}-x^{2}y^{3}-2xy^{4}}{x^{4}y^{2}-x^{2}y^4-2x^3y^3+2xy^5}

$$\frac { x ^ { 3 } y ^ { 2 } - x ^ { 2 } y ^ { 3 } - 2 x y ^ { 4 } } { x ^ { 4 } y ^ { 2 } - x ^ { 2 } y ^ { 4 } - 2 x ^ { 3 } y ^ { 3 } + 2 x y ^ { 5 } }$$

Evaluate

$$\frac{1}{x-y}$$

Short Solution Steps

Factor the expressions that are not already factored.

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

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

$$\frac{1}{x-y}$$

Expand

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

Short Solution Steps

Factor the expressions that are not already factored.

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

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

$$\frac{1}{x-y}$$