Solve x^2-36/2x+12*2/x^2-2x-24

$$\frac { x ^ { 2 } - 36 } { 2 x + 12 } \cdot \frac { 2 } { x ^ { 2 } - 2 x - 24 }$$

Evaluate

$$\frac{1}{x+4}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{x^{2}-36}{2x+12}.

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

Cancel out x+6 in both numerator and denominator.

$$\frac{x-6}{2}\times \frac{2}{x^{2}-2x-24}$$

Multiply \frac{x-6}{2} times \frac{2}{x^{2}-2x-24} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(x-6\right)\times 2}{2\left(x^{2}-2x-24\right)}$$

Cancel out 2 in both numerator and denominator.

$$\frac{x-6}{x^{2}-2x-24}$$

Factor the expressions that are not already factored.

$$\frac{x-6}{\left(x-6\right)\left(x+4\right)}$$

Cancel out x-6 in both numerator and denominator.

$$\frac{1}{x+4}$$

Expand

$$\frac{1}{x+4}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{x^{2}-36}{2x+12}.

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

Cancel out x+6 in both numerator and denominator.

$$\frac{x-6}{2}\times \frac{2}{x^{2}-2x-24}$$

Multiply \frac{x-6}{2} times \frac{2}{x^{2}-2x-24} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(x-6\right)\times 2}{2\left(x^{2}-2x-24\right)}$$

Cancel out 2 in both numerator and denominator.

$$\frac{x-6}{x^{2}-2x-24}$$

Factor the expressions that are not already factored.

$$\frac{x-6}{\left(x-6\right)\left(x+4\right)}$$

Cancel out x-6 in both numerator and denominator.

$$\frac{1}{x+4}$$