Solve frac{2x^{3}+2x^2-12x}{4x^3-8x^2}*2x-6/x^2-9

$$\frac { 2 x ^ { 3 } + 2 x ^ { 2 } - 12 x } { 4 x ^ { 3 } - 8 x ^ { 2 } } \cdot \frac { 2 x - 6 } { x ^ { 2 } - 9 }$$

Evaluate

$$\frac{1}{x}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{2x^{3}+2x^{2}-12x}{4x^{3}-8x^{2}}.

$$\frac{2x\left(x-2\right)\left(x+3\right)}{4\left(x-2\right)x^{2}}\times \frac{2x-6}{x^{2}-9}$$

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

$$\frac{x+3}{2x}\times \frac{2x-6}{x^{2}-9}$$

Factor the expressions that are not already factored in \frac{2x-6}{x^{2}-9}.

$$\frac{x+3}{2x}\times \frac{2\left(x-3\right)}{\left(x-3\right)\left(x+3\right)}$$

Cancel out x-3 in both numerator and denominator.

$$\frac{x+3}{2x}\times \frac{2}{x+3}$$

Multiply \frac{x+3}{2x} times \frac{2}{x+3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(x+3\right)\times 2}{2x\left(x+3\right)}$$

Cancel out 2\left(x+3\right) in both numerator and denominator.

$$\frac{1}{x}$$

Expand

$$\frac{1}{x}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{2x^{3}+2x^{2}-12x}{4x^{3}-8x^{2}}.

$$\frac{2x\left(x-2\right)\left(x+3\right)}{4\left(x-2\right)x^{2}}\times \frac{2x-6}{x^{2}-9}$$

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

$$\frac{x+3}{2x}\times \frac{2x-6}{x^{2}-9}$$

Factor the expressions that are not already factored in \frac{2x-6}{x^{2}-9}.

$$\frac{x+3}{2x}\times \frac{2\left(x-3\right)}{\left(x-3\right)\left(x+3\right)}$$

Cancel out x-3 in both numerator and denominator.

$$\frac{x+3}{2x}\times \frac{2}{x+3}$$

Multiply \frac{x+3}{2x} times \frac{2}{x+3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(x+3\right)\times 2}{2x\left(x+3\right)}$$

Cancel out 2\left(x+3\right) in both numerator and denominator.

$$\frac{1}{x}$$