Solve x^2+7x+12/x^2-9divx+4/2x-6

$$\frac { x ^ { 2 } + 7 x + 12 } { x ^ { 2 } - 9 } \div \frac { x + 4 } { 2 x - 6 }$$

Evaluate

$$2$$

Short Solution Steps

Divide \frac{x^{2}+7x+12}{x^{2}-9} by \frac{x+4}{2x-6} by multiplying \frac{x^{2}+7x+12}{x^{2}-9} by the reciprocal of \frac{x+4}{2x-6}.

$$\frac{\left(x^{2}+7x+12\right)\left(2x-6\right)}{\left(x^{2}-9\right)\left(x+4\right)}$$

Factor the expressions that are not already factored.

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

Cancel out \left(x-3\right)\left(x+3\right)\left(x+4\right) in both numerator and denominator.

$$2$$

Factor

$$2$$