Solve -4x^2+4/2x-6x-8div6x^2-12x+6/6x-24

$$\frac { - 4 x ^ { 2 } + 4 } { 2 x - 6 x - 8 } \div \frac { 6 x ^ { 2 } - 12 x + 6 } { 6 x - 24 }$$

Evaluate

$$\frac{\left(x-4\right)\left(x+1\right)}{\left(x-1\right)\left(x+2\right)}$$

Short Solution Steps

Divide \frac{-4x^{2}+4}{2x-6x-8} by \frac{6x^{2}-12x+6}{6x-24} by multiplying \frac{-4x^{2}+4}{2x-6x-8} by the reciprocal of \frac{6x^{2}-12x+6}{6x-24}.

$$\frac{\left(-4x^{2}+4\right)\left(6x-24\right)}{\left(2x-6x-8\right)\left(6x^{2}-12x+6\right)}$$

Combine 2x and -6x to get -4x.

$$\frac{\left(-4x^{2}+4\right)\left(6x-24\right)}{\left(-4x-8\right)\left(6x^{2}-12x+6\right)}$$

Factor the expressions that are not already factored.

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

Cancel out 4\times 6\left(x-1\right) in both numerator and denominator.

$$\frac{\left(x-4\right)\left(-x-1\right)}{\left(x-1\right)\left(-x-2\right)}$$

Expand the expression.

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

Expand

$$\frac{x^{2}-3x-4}{\left(x-1\right)\left(x+2\right)}$$

Short Solution Steps

Divide \frac{-4x^{2}+4}{2x-6x-8} by \frac{6x^{2}-12x+6}{6x-24} by multiplying \frac{-4x^{2}+4}{2x-6x-8} by the reciprocal of \frac{6x^{2}-12x+6}{6x-24}.

$$\frac{\left(-4x^{2}+4\right)\left(6x-24\right)}{\left(2x-6x-8\right)\left(6x^{2}-12x+6\right)}$$

Combine 2x and -6x to get -4x.

$$\frac{\left(-4x^{2}+4\right)\left(6x-24\right)}{\left(-4x-8\right)\left(6x^{2}-12x+6\right)}$$

Factor the expressions that are not already factored.

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

Cancel out 4\times 6\left(x-1\right) in both numerator and denominator.

$$\frac{\left(x-4\right)\left(-x-1\right)}{\left(x-1\right)\left(-x-2\right)}$$

Expand the expression.

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