Solve x^2-9/x^2+4x+2:x-3/x+2

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

Evaluate

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

Short Solution Steps

Divide \frac{x^{2}-9}{x^{2}+4x+2} by \frac{x-3}{x+2} by multiplying \frac{x^{2}-9}{x^{2}+4x+2} by the reciprocal of \frac{x-3}{x+2}.

$$\frac{\left(x^{2}-9\right)\left(x+2\right)}{\left(x^{2}+4x+2\right)\left(x-3\right)}$$

Factor the expressions that are not already factored.

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

Cancel out x-3 in both numerator and denominator.

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

Expand the expression.

$$\frac{x^{2}+5x+6}{x^{2}+4x+2}$$

Expand

$$\frac{x^{2}+5x+6}{x^{2}+4x+2}$$

Short Solution Steps

Divide \frac{x^{2}-9}{x^{2}+4x+2} by \frac{x-3}{x+2} by multiplying \frac{x^{2}-9}{x^{2}+4x+2} by the reciprocal of \frac{x-3}{x+2}.

$$\frac{\left(x^{2}-9\right)\left(x+2\right)}{\left(x^{2}+4x+2\right)\left(x-3\right)}$$

Factor the expressions that are not already factored.

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

Cancel out x-3 in both numerator and denominator.

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

Expand the expression.

$$\frac{x^{2}+5x+6}{x^{2}+4x+2}$$