Solve x^2x-6/x^2-4divx^2+3x/x^2+2x=

$$\frac { x ^ { 2 } x - 6 } { x ^ { 2 } - 4 } \div \frac { x ^ { 2 } + 3 x } { x ^ { 2 } + 2 x } =$$

Evaluate

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

Short Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

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

Divide \frac{x^{3}-6}{x^{2}-4} by \frac{x^{2}+3x}{x^{2}+2x} by multiplying \frac{x^{3}-6}{x^{2}-4} by the reciprocal of \frac{x^{2}+3x}{x^{2}+2x}.

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

Factor the expressions that are not already factored.

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

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

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

Expand the expression.

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

Expand

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

Short Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

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

Divide \frac{x^{3}-6}{x^{2}-4} by \frac{x^{2}+3x}{x^{2}+2x} by multiplying \frac{x^{3}-6}{x^{2}-4} by the reciprocal of \frac{x^{2}+3x}{x^{2}+2x}.

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

Factor the expressions that are not already factored.

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

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

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

Expand the expression.

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