Solve (x^2-2x/x^2-4x+4-4/x-2)divx-4/x^2-4

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

Evaluate

$$x+2$$

Short Solution Steps

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

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

Cancel out x-2 in both numerator and denominator.

$$\frac{\frac{x}{x-2}-\frac{4}{x-2}}{\frac{x-4}{x^{2}-4}}$$

Since \frac{x}{x-2} and \frac{4}{x-2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{x-4}{x-2}}{\frac{x-4}{x^{2}-4}}$$

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

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

Cancel out x-4 in both numerator and denominator.

$$\frac{x^{2}-4}{x-2}$$

Factor the expressions that are not already factored.

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

Cancel out x-2 in both numerator and denominator.

$$x+2$$

Expand

$$x+2$$

Short Solution Steps

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

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

Cancel out x-2 in both numerator and denominator.

$$\frac{\frac{x}{x-2}-\frac{4}{x-2}}{\frac{x-4}{x^{2}-4}}$$

Since \frac{x}{x-2} and \frac{4}{x-2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{x-4}{x-2}}{\frac{x-4}{x^{2}-4}}$$

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

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

Cancel out x-4 in both numerator and denominator.

$$\frac{x^{2}-4}{x-2}$$

Factor the expressions that are not already factored.

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

Cancel out x-2 in both numerator and denominator.

$$x+2$$