Solve x^2-x-12/x^2-3x-10divx^2-9x+20/x^2-2x-8*x-5/x+3

$$\frac { x ^ { 2 } - x - 12 } { x ^ { 2 } - 3 x - 10 } \div \frac { x ^ { 2 } - 9 x + 20 } { x ^ { 2 } - 2 x - 8 } \times \frac { x - 5 } { x + 3 }$$

Evaluate

$$\frac{x-4}{x-5}$$

Short Solution Steps

Divide \frac{x^{2}-x-12}{x^{2}-3x-10} by \frac{x^{2}-9x+20}{x^{2}-2x-8} by multiplying \frac{x^{2}-x-12}{x^{2}-3x-10} by the reciprocal of \frac{x^{2}-9x+20}{x^{2}-2x-8}.

$$\frac{\left(x^{2}-x-12\right)\left(x^{2}-2x-8\right)}{\left(x^{2}-3x-10\right)\left(x^{2}-9x+20\right)}\times \frac{x-5}{x+3}$$

Factor the expressions that are not already factored in \frac{\left(x^{2}-x-12\right)\left(x^{2}-2x-8\right)}{\left(x^{2}-3x-10\right)\left(x^{2}-9x+20\right)}.

$$\frac{\left(x+2\right)\left(x+3\right)\left(x-4\right)^{2}}{\left(x-4\right)\left(x+2\right)\left(x-5\right)^{2}}\times \frac{x-5}{x+3}$$

Cancel out \left(x-4\right)\left(x+2\right) in both numerator and denominator.

$$\frac{\left(x-4\right)\left(x+3\right)}{\left(x-5\right)^{2}}\times \frac{x-5}{x+3}$$

Multiply \frac{\left(x-4\right)\left(x+3\right)}{\left(x-5\right)^{2}} times \frac{x-5}{x+3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(x-4\right)\left(x+3\right)\left(x-5\right)}{\left(x-5\right)^{2}\left(x+3\right)}$$

Cancel out \left(x-5\right)\left(x+3\right) in both numerator and denominator.

$$\frac{x-4}{x-5}$$

Expand

$$\frac{x-4}{x-5}$$

Short Solution Steps

Divide \frac{x^{2}-x-12}{x^{2}-3x-10} by \frac{x^{2}-9x+20}{x^{2}-2x-8} by multiplying \frac{x^{2}-x-12}{x^{2}-3x-10} by the reciprocal of \frac{x^{2}-9x+20}{x^{2}-2x-8}.

$$\frac{\left(x^{2}-x-12\right)\left(x^{2}-2x-8\right)}{\left(x^{2}-3x-10\right)\left(x^{2}-9x+20\right)}\times \frac{x-5}{x+3}$$

Factor the expressions that are not already factored in \frac{\left(x^{2}-x-12\right)\left(x^{2}-2x-8\right)}{\left(x^{2}-3x-10\right)\left(x^{2}-9x+20\right)}.

$$\frac{\left(x+2\right)\left(x+3\right)\left(x-4\right)^{2}}{\left(x-4\right)\left(x+2\right)\left(x-5\right)^{2}}\times \frac{x-5}{x+3}$$

Cancel out \left(x-4\right)\left(x+2\right) in both numerator and denominator.

$$\frac{\left(x-4\right)\left(x+3\right)}{\left(x-5\right)^{2}}\times \frac{x-5}{x+3}$$

Multiply \frac{\left(x-4\right)\left(x+3\right)}{\left(x-5\right)^{2}} times \frac{x-5}{x+3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(x-4\right)\left(x+3\right)\left(x-5\right)}{\left(x-5\right)^{2}\left(x+3\right)}$$

Cancel out \left(x-5\right)\left(x+3\right) in both numerator and denominator.

$$\frac{x-4}{x-5}$$