Solve x^2-x-2/x^2+x-12*x^2-3x/x^2-4x+1

$$\frac { x ^ { 2 } - x - 2 } { x ^ { 2 } + x - 12 } \cdot \frac { x ^ { 2 } - 3 x } { x ^ { 2 } - 4 x + 1 }$$

Evaluate

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

Short Solution Steps

Multiply \frac{x^{2}-x-2}{x^{2}+x-12} times \frac{x^{2}-3x}{x^{2}-4x+1} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(x^{2}-x-2\right)\left(x^{2}-3x\right)}{\left(x^{2}+x-12\right)\left(x^{2}-4x+1\right)}$$

Factor the expressions that are not already factored.

$$\frac{x\left(x-3\right)\left(x-2\right)\left(x+1\right)}{\left(x-3\right)\left(x+4\right)\left(x-\left(\sqrt{3}+2\right)\right)\left(x-\left(-\sqrt{3}+2\right)\right)}$$

Cancel out x-3 in both numerator and denominator.

$$\frac{x\left(x-2\right)\left(x+1\right)}{\left(x+4\right)\left(x-\left(\sqrt{3}+2\right)\right)\left(x-\left(-\sqrt{3}+2\right)\right)}$$

Expand the expression.

$$\frac{x^{3}-x^{2}-2x}{x^{3}-15x+4}$$

Expand

$$\frac{x^{3}-x^{2}-2x}{\left(x+4\right)\left(x^{2}-4x+1\right)}$$

Short Solution Steps

Multiply \frac{x^{2}-x-2}{x^{2}+x-12} times \frac{x^{2}-3x}{x^{2}-4x+1} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(x^{2}-x-2\right)\left(x^{2}-3x\right)}{\left(x^{2}+x-12\right)\left(x^{2}-4x+1\right)}$$

Factor the expressions that are not already factored.

$$\frac{x\left(x-3\right)\left(x-2\right)\left(x+1\right)}{\left(x-3\right)\left(x+4\right)\left(x-\left(\sqrt{3}+2\right)\right)\left(x-\left(-\sqrt{3}+2\right)\right)}$$

Cancel out x-3 in both numerator and denominator.

$$\frac{x\left(x-2\right)\left(x+1\right)}{\left(x+4\right)\left(x-\left(\sqrt{3}+2\right)\right)\left(x-\left(-\sqrt{3}+2\right)\right)}$$

Expand the expression.

$$\frac{x^{3}-x^{2}-2x}{x^{3}-15x+4}$$