Solve x^2-3x+2/x^2+3x-10*x^2-x-30/x^2-2x-24

$$\frac { x ^ { 2 } - 3 x + 2 } { x ^ { 2 } + 3 x - 10 } \cdot \frac { x ^ { 2 } - x - 30 } { x ^ { 2 } - 2 x - 24 }$$

Evaluate

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

Short Solution Steps

Factor the expressions that are not already factored in \frac{x^{2}-3x+2}{x^{2}+3x-10}.

$$\frac{\left(x-2\right)\left(x-1\right)}{\left(x-2\right)\left(x+5\right)}\times \frac{x^{2}-x-30}{x^{2}-2x-24}$$

Cancel out x-2 in both numerator and denominator.

$$\frac{x-1}{x+5}\times \frac{x^{2}-x-30}{x^{2}-2x-24}$$

Factor the expressions that are not already factored in \frac{x^{2}-x-30}{x^{2}-2x-24}.

$$\frac{x-1}{x+5}\times \frac{\left(x-6\right)\left(x+5\right)}{\left(x-6\right)\left(x+4\right)}$$

Cancel out x-6 in both numerator and denominator.

$$\frac{x-1}{x+5}\times \frac{x+5}{x+4}$$

Multiply \frac{x-1}{x+5} times \frac{x+5}{x+4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(x-1\right)\left(x+5\right)}{\left(x+5\right)\left(x+4\right)}$$

Cancel out x+5 in both numerator and denominator.

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

Expand

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

Short Solution Steps

Factor the expressions that are not already factored in \frac{x^{2}-3x+2}{x^{2}+3x-10}.

$$\frac{\left(x-2\right)\left(x-1\right)}{\left(x-2\right)\left(x+5\right)}\times \frac{x^{2}-x-30}{x^{2}-2x-24}$$

Cancel out x-2 in both numerator and denominator.

$$\frac{x-1}{x+5}\times \frac{x^{2}-x-30}{x^{2}-2x-24}$$

Factor the expressions that are not already factored in \frac{x^{2}-x-30}{x^{2}-2x-24}.

$$\frac{x-1}{x+5}\times \frac{\left(x-6\right)\left(x+5\right)}{\left(x-6\right)\left(x+4\right)}$$

Cancel out x-6 in both numerator and denominator.

$$\frac{x-1}{x+5}\times \frac{x+5}{x+4}$$

Multiply \frac{x-1}{x+5} times \frac{x+5}{x+4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(x-1\right)\left(x+5\right)}{\left(x+5\right)\left(x+4\right)}$$

Cancel out x+5 in both numerator and denominator.

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