Solve x+6/x-1*x^2-4x-12/x^2-xdivx^2+8x+12/x-6

$$\frac { x + 6 } { x - 1 } \times \frac { x ^ { 2 } - 4 x - 12 } { x ^ { 2 } - x } \div \frac { x ^ { 2 } + 8 x + 12 } { x - 6 }$$

Evaluate

$$\frac{\left(\frac{x-6}{x-1}\right)^{2}}{x}$$

Short Solution Steps

Multiply \frac{x+6}{x-1} times \frac{x^{2}-4x-12}{x^{2}-x} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{\left(x+6\right)\left(x^{2}-4x-12\right)}{\left(x-1\right)\left(x^{2}-x\right)}}{\frac{x^{2}+8x+12}{x-6}}$$

Divide \frac{\left(x+6\right)\left(x^{2}-4x-12\right)}{\left(x-1\right)\left(x^{2}-x\right)} by \frac{x^{2}+8x+12}{x-6} by multiplying \frac{\left(x+6\right)\left(x^{2}-4x-12\right)}{\left(x-1\right)\left(x^{2}-x\right)} by the reciprocal of \frac{x^{2}+8x+12}{x-6}.

$$\frac{\left(x+6\right)\left(x^{2}-4x-12\right)\left(x-6\right)}{\left(x-1\right)\left(x^{2}-x\right)\left(x^{2}+8x+12\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(x+2\right)\left(x+6\right)\left(x-6\right)^{2}}{x\left(x+2\right)\left(x+6\right)\left(x-1\right)^{2}}$$

Cancel out \left(x+2\right)\left(x+6\right) in both numerator and denominator.

$$\frac{\left(x-6\right)^{2}}{x\left(x-1\right)^{2}}$$

Expand the expression.

$$\frac{x^{2}-12x+36}{x^{3}-2x^{2}+x}$$

Expand

$$\frac{x^{2}-12x+36}{\left(x-1\right)\left(x^{2}-x\right)}$$

Short Solution Steps

Multiply \frac{x+6}{x-1} times \frac{x^{2}-4x-12}{x^{2}-x} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{\left(x+6\right)\left(x^{2}-4x-12\right)}{\left(x-1\right)\left(x^{2}-x\right)}}{\frac{x^{2}+8x+12}{x-6}}$$

Divide \frac{\left(x+6\right)\left(x^{2}-4x-12\right)}{\left(x-1\right)\left(x^{2}-x\right)} by \frac{x^{2}+8x+12}{x-6} by multiplying \frac{\left(x+6\right)\left(x^{2}-4x-12\right)}{\left(x-1\right)\left(x^{2}-x\right)} by the reciprocal of \frac{x^{2}+8x+12}{x-6}.

$$\frac{\left(x+6\right)\left(x^{2}-4x-12\right)\left(x-6\right)}{\left(x-1\right)\left(x^{2}-x\right)\left(x^{2}+8x+12\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(x+2\right)\left(x+6\right)\left(x-6\right)^{2}}{x\left(x+2\right)\left(x+6\right)\left(x-1\right)^{2}}$$

Cancel out \left(x+2\right)\left(x+6\right) in both numerator and denominator.

$$\frac{\left(x-6\right)^{2}}{x\left(x-1\right)^{2}}$$

Expand the expression.

$$\frac{x^{2}-12x+36}{x^{3}-2x^{2}+x}$$