Solve 2x^2+7x-4/x^2-36*x^2-4x-12/x^2+6x+8

$$\frac { 2 x ^ { 2 } + 7 x - 4 } { x ^ { 2 } - 36 } \times \frac { x ^ { 2 } - 4 x - 12 } { x ^ { 2 } + 6 x + 8 }$$

Evaluate

$$\frac{2x-1}{x+6}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{x^{2}-4x-12}{x^{2}+6x+8}.

$$\frac{2x^{2}+7x-4}{x^{2}-36}\times \frac{\left(x-6\right)\left(x+2\right)}{\left(x+2\right)\left(x+4\right)}$$

Cancel out x+2 in both numerator and denominator.

$$\frac{2x^{2}+7x-4}{x^{2}-36}\times \frac{x-6}{x+4}$$

Multiply \frac{2x^{2}+7x-4}{x^{2}-36} times \frac{x-6}{x+4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(2x^{2}+7x-4\right)\left(x-6\right)}{\left(x^{2}-36\right)\left(x+4\right)}$$

Factor the expressions that are not already factored.

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

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

$$\frac{2x-1}{x+6}$$

Expand

$$\frac{2x-1}{x+6}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{x^{2}-4x-12}{x^{2}+6x+8}.

$$\frac{2x^{2}+7x-4}{x^{2}-36}\times \frac{\left(x-6\right)\left(x+2\right)}{\left(x+2\right)\left(x+4\right)}$$

Cancel out x+2 in both numerator and denominator.

$$\frac{2x^{2}+7x-4}{x^{2}-36}\times \frac{x-6}{x+4}$$

Multiply \frac{2x^{2}+7x-4}{x^{2}-36} times \frac{x-6}{x+4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(2x^{2}+7x-4\right)\left(x-6\right)}{\left(x^{2}-36\right)\left(x+4\right)}$$

Factor the expressions that are not already factored.

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

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

$$\frac{2x-1}{x+6}$$