Solve frac{y^{3}x^{2}+4x^{2}y+2y^2x^2+8x^2}{xy^4-16x}

$$\frac { y ^ { 3 } x ^ { 2 } + 4 x ^ { 2 } y + 2 y ^ { 2 } x ^ { 2 } + 8 x ^ { 2 } } { x y ^ { 4 } - 16 x }$$

Evaluate

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

Short Solution Steps

Factor the expressions that are not already factored.

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

Cancel out x\left(y+2\right)\left(y^{2}+4\right) in both numerator and denominator.

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

Expand

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

Short Solution Steps

Factor the expressions that are not already factored.

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

Cancel out x\left(y+2\right)\left(y^{2}+4\right) in both numerator and denominator.

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