Solve (x-3)^2/x+2:2x*6/x^2-4=

$$\frac { ( x - 3 ) ^ { 2 } } { x + 2 } : \frac { 2 x \cdot 6 } { x ^ { 2 } - 4 } =$$

Evaluate

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

Short Solution Steps

Divide \frac{\left(x-3\right)^{2}}{x+2} by \frac{2x\times 6}{x^{2}-4} by multiplying \frac{\left(x-3\right)^{2}}{x+2} by the reciprocal of \frac{2x\times 6}{x^{2}-4}.

$$\frac{\left(x-3\right)^{2}\left(x^{2}-4\right)}{\left(x+2\right)\times 2x\times 6}$$

Multiply 2 and 6 to get 12.

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

Factor the expressions that are not already factored.

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

Cancel out x+2 in both numerator and denominator.

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

Expand the expression.

$$\frac{x^{3}-8x^{2}+21x-18}{12x}$$

Expand

$$\frac{x^{2}}{12}-\frac{2x}{3}+\frac{7}{4}-\frac{3}{2x}$$

Short Solution Steps

Divide \frac{\left(x-3\right)^{2}}{x+2} by \frac{2x\times 6}{x^{2}-4} by multiplying \frac{\left(x-3\right)^{2}}{x+2} by the reciprocal of \frac{2x\times 6}{x^{2}-4}.

$$\frac{\left(x-3\right)^{2}\left(x^{2}-4\right)}{\left(x+2\right)\times 2x\times 6}$$

Multiply 2 and 6 to get 12.

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

Factor the expressions that are not already factored.

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

Cancel out x+2 in both numerator and denominator.

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

Expand the expression.

$$\frac{x^{3}-8x^{2}+21x-18}{12x}$$