Solve x^2+5x-6/x^2-1*x^2+x/x^2+8x+12

$$\frac { x ^ { 2 } + 5 x - 6 } { x ^ { 2 } - 1 } \cdot \frac { x ^ { 2 } + x } { x ^ { 2 } + 8 x + 12 }$$

Evaluate

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

Short Solution Steps

Factor the expressions that are not already factored in \frac{x^{2}+5x-6}{x^{2}-1}.

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

Cancel out x-1 in both numerator and denominator.

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

Multiply \frac{x+6}{x+1} times \frac{x^{2}+x}{x^{2}+8x+12} by multiplying numerator times numerator and denominator times denominator.

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

Factor the expressions that are not already factored.

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

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

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

Expand

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

Short Solution Steps

Factor the expressions that are not already factored in \frac{x^{2}+5x-6}{x^{2}-1}.

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

Cancel out x-1 in both numerator and denominator.

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

Multiply \frac{x+6}{x+1} times \frac{x^{2}+x}{x^{2}+8x+12} by multiplying numerator times numerator and denominator times denominator.

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

Factor the expressions that are not already factored.

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

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

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