Solve x^2-4x/x^2-8x+16/frac{12{2x-8}}

$$\frac { \frac { x ^ { 2 } - 4 x } { x ^ { 2 } - 8 x + 16 } } { \frac { 12 } { 2 x - 8 } }$$

Evaluate

$$\frac{x}{6}$$

Short Solution Steps

Divide \frac{x^{2}-4x}{x^{2}-8x+16} by \frac{12}{2x-8} by multiplying \frac{x^{2}-4x}{x^{2}-8x+16} by the reciprocal of \frac{12}{2x-8}.

$$\frac{\left(x^{2}-4x\right)\left(2x-8\right)}{\left(x^{2}-8x+16\right)\times 12}$$

Factor the expressions that are not already factored.

$$\frac{2x\left(x-4\right)^{2}}{12\left(x-4\right)^{2}}$$

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

$$\frac{x}{6}$$

Expand

$$\frac{x}{6}$$

Short Solution Steps

Divide \frac{x^{2}-4x}{x^{2}-8x+16} by \frac{12}{2x-8} by multiplying \frac{x^{2}-4x}{x^{2}-8x+16} by the reciprocal of \frac{12}{2x-8}.

$$\frac{\left(x^{2}-4x\right)\left(2x-8\right)}{\left(x^{2}-8x+16\right)\times 12}$$

Factor the expressions that are not already factored.

$$\frac{2x\left(x-4\right)^{2}}{12\left(x-4\right)^{2}}$$

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

$$\frac{x}{6}$$