Solve x^2-12x+32/x-4*x/x-8

$$\frac { x ^ { 2 } - 12 x + 32 } { x - 4 } \cdot \frac { x } { x - 8 }$$

Evaluate

$$x$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{x^{2}-12x+32}{x-4}.

$$\frac{\left(x-8\right)\left(x-4\right)}{x-4}\times \frac{x}{x-8}$$

Cancel out x-4 in both numerator and denominator.

$$\left(x-8\right)\times \frac{x}{x-8}$$

Cancel out x-8 and x-8.

$$x$$

Differentiate w.r.t. x

$$1$$

Steps Using Definition of a Derivative

Factor the expressions that are not already factored in \frac{x^{2}-12x+32}{x-4}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{\left(x-8\right)\left(x-4\right)}{x-4}\times \frac{x}{x-8})$$

Cancel out x-4 in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\left(x-8\right)\times \frac{x}{x-8})$$

Cancel out x-8 and x-8.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x)$$

The derivative of ax^{n} is nax^{n-1}.

$$x^{1-1}$$

Subtract 1 from 1.

$$x^{0}$$

For any term t except 0, t^{0}=1.

$$1$$