Solve x^2-x-2/3x^2*3x-12/x^2-6x+8

$$\frac { x ^ { 2 } - x - 2 } { 3 x ^ { 2 } } \cdot \frac { 3 x - 12 } { x ^ { 2 } - 6 x + 8 }$$

Evaluate

$$\frac{x+1}{x^{2}}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{3x-12}{x^{2}-6x+8}.

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

Cancel out x-4 in both numerator and denominator.

$$\frac{x^{2}-x-2}{3x^{2}}\times \frac{3}{x-2}$$

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

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

Cancel out 3 in both numerator and denominator.

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

Factor the expressions that are not already factored.

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

Cancel out x-2 in both numerator and denominator.

$$\frac{x+1}{x^{2}}$$

Expand

$$\frac{x+1}{x^{2}}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{3x-12}{x^{2}-6x+8}.

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

Cancel out x-4 in both numerator and denominator.

$$\frac{x^{2}-x-2}{3x^{2}}\times \frac{3}{x-2}$$

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

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

Cancel out 3 in both numerator and denominator.

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

Factor the expressions that are not already factored.

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

Cancel out x-2 in both numerator and denominator.

$$\frac{x+1}{x^{2}}$$