Solve x^2-6x+9/3x-6*x^2-x-6/x^2-4

$$\frac { x ^ { 2 } - 6 x + 9 } { 3 x - 6 } \cdot \frac { x ^ { 2 } - x - 6 } { x ^ { 2 } - 4 }$$

Evaluate

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

Short Solution Steps

Factor the expressions that are not already factored in \frac{x^{2}-x-6}{x^{2}-4}.

$$\frac{x^{2}-6x+9}{3x-6}\times \frac{\left(x-3\right)\left(x+2\right)}{\left(x-2\right)\left(x+2\right)}$$

Cancel out x+2 in both numerator and denominator.

$$\frac{x^{2}-6x+9}{3x-6}\times \frac{x-3}{x-2}$$

Multiply \frac{x^{2}-6x+9}{3x-6} times \frac{x-3}{x-2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(x^{2}-6x+9\right)\left(x-3\right)}{\left(3x-6\right)\left(x-2\right)}$$

Use the distributive property to multiply x^{2}-6x+9 by x-3 and combine like terms.

$$\frac{x^{3}-9x^{2}+27x-27}{\left(3x-6\right)\left(x-2\right)}$$

Use the distributive property to multiply 3x-6 by x-2 and combine like terms.

$$\frac{x^{3}-9x^{2}+27x-27}{3x^{2}-12x+12}$$

Expand

$$\frac{x^{3}-9x^{2}+27x-27}{3\left(x-2\right)^{2}}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{x^{2}-x-6}{x^{2}-4}.

$$\frac{x^{2}-6x+9}{3x-6}\times \frac{\left(x-3\right)\left(x+2\right)}{\left(x-2\right)\left(x+2\right)}$$

Cancel out x+2 in both numerator and denominator.

$$\frac{x^{2}-6x+9}{3x-6}\times \frac{x-3}{x-2}$$

Multiply \frac{x^{2}-6x+9}{3x-6} times \frac{x-3}{x-2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(x^{2}-6x+9\right)\left(x-3\right)}{\left(3x-6\right)\left(x-2\right)}$$

Use the distributive property to multiply x^{2}-6x+9 by x-3 and combine like terms.

$$\frac{x^{3}-9x^{2}+27x-27}{\left(3x-6\right)\left(x-2\right)}$$

Use the distributive property to multiply 3x-6 by x-2 and combine like terms.

$$\frac{x^{3}-9x^{2}+27x-27}{3x^{2}-12x+12}$$