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

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

Evaluate

$$\frac{x+3}{x}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{x^{2}-9}{x^{2}-x-6}.

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

Cancel out x-3 in both numerator and denominator.

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

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

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

Cancel out x in both numerator and denominator.

$$\frac{x+3}{x+2}\times \frac{x+2}{x}$$

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

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

Cancel out x+2 in both numerator and denominator.

$$\frac{x+3}{x}$$

Expand

$$\frac{x+3}{x}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{x^{2}-9}{x^{2}-x-6}.

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

Cancel out x-3 in both numerator and denominator.

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

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

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

Cancel out x in both numerator and denominator.

$$\frac{x+3}{x+2}\times \frac{x+2}{x}$$

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

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

Cancel out x+2 in both numerator and denominator.

$$\frac{x+3}{x}$$