Solve x^2-x-6/x^2+5x+6*x^2-x-12/x^2-10x+24

$$\frac { x ^ { 2 } - x - 6 } { x ^ { 2 } + 5 x + 6 } \cdot \frac { x ^ { 2 } - x - 12 } { x ^ { 2 } - 10 x + 24 }$$

Evaluate

$$\frac{x-3}{x-6}$$

Short Solution Steps

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

$$\frac{\left(x-3\right)\left(x+2\right)}{\left(x+2\right)\left(x+3\right)}\times \frac{x^{2}-x-12}{x^{2}-10x+24}$$

Cancel out x+2 in both numerator and denominator.

$$\frac{x-3}{x+3}\times \frac{x^{2}-x-12}{x^{2}-10x+24}$$

Factor the expressions that are not already factored in \frac{x^{2}-x-12}{x^{2}-10x+24}.

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

Cancel out x-4 in both numerator and denominator.

$$\frac{x-3}{x+3}\times \frac{x+3}{x-6}$$

Multiply \frac{x-3}{x+3} times \frac{x+3}{x-6} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(x-3\right)\left(x+3\right)}{\left(x+3\right)\left(x-6\right)}$$

Cancel out x+3 in both numerator and denominator.

$$\frac{x-3}{x-6}$$

Expand

$$\frac{x-3}{x-6}$$

Short Solution Steps

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

$$\frac{\left(x-3\right)\left(x+2\right)}{\left(x+2\right)\left(x+3\right)}\times \frac{x^{2}-x-12}{x^{2}-10x+24}$$

Cancel out x+2 in both numerator and denominator.

$$\frac{x-3}{x+3}\times \frac{x^{2}-x-12}{x^{2}-10x+24}$$

Factor the expressions that are not already factored in \frac{x^{2}-x-12}{x^{2}-10x+24}.

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

Cancel out x-4 in both numerator and denominator.

$$\frac{x-3}{x+3}\times \frac{x+3}{x-6}$$

Multiply \frac{x-3}{x+3} times \frac{x+3}{x-6} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(x-3\right)\left(x+3\right)}{\left(x+3\right)\left(x-6\right)}$$

Cancel out x+3 in both numerator and denominator.

$$\frac{x-3}{x-6}$$