Solve x^2-4x+4/x^2-4*4x^3y/4xy-8y

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

Evaluate

$$\frac{x^{3}}{x+2}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{x^{2}-4x+4}{x^{2}-4}.

$$\frac{\left(x-2\right)^{2}}{\left(x-2\right)\left(x+2\right)}\times \frac{4x^{3}y}{4xy-8y}$$

Cancel out x-2 in both numerator and denominator.

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

Factor the expressions that are not already factored in \frac{4x^{3}y}{4xy-8y}.

$$\frac{x-2}{x+2}\times \frac{4yx^{3}}{4y\left(x-2\right)}$$

Cancel out 4y in both numerator and denominator.

$$\frac{x-2}{x+2}\times \frac{x^{3}}{x-2}$$

Multiply \frac{x-2}{x+2} times \frac{x^{3}}{x-2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(x-2\right)x^{3}}{\left(x+2\right)\left(x-2\right)}$$

Cancel out x-2 in both numerator and denominator.

$$\frac{x^{3}}{x+2}$$

Expand

$$\frac{x^{3}}{x+2}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{x^{2}-4x+4}{x^{2}-4}.

$$\frac{\left(x-2\right)^{2}}{\left(x-2\right)\left(x+2\right)}\times \frac{4x^{3}y}{4xy-8y}$$

Cancel out x-2 in both numerator and denominator.

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

Factor the expressions that are not already factored in \frac{4x^{3}y}{4xy-8y}.

$$\frac{x-2}{x+2}\times \frac{4yx^{3}}{4y\left(x-2\right)}$$

Cancel out 4y in both numerator and denominator.

$$\frac{x-2}{x+2}\times \frac{x^{3}}{x-2}$$

Multiply \frac{x-2}{x+2} times \frac{x^{3}}{x-2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(x-2\right)x^{3}}{\left(x+2\right)\left(x-2\right)}$$

Cancel out x-2 in both numerator and denominator.

$$\frac{x^{3}}{x+2}$$