Solve c^2+3c+2/c^2+7c+12:c^2-1/c^2-9=

$$\frac { c ^ { 2 } + 3 c + 2 } { c ^ { 2 } + 7 c + 12 } : \frac { c ^ { 2 } - 1 } { c ^ { 2 } - 9 } =$$

Evaluate

$$\frac{\left(c-3\right)\left(c+2\right)}{\left(c-1\right)\left(c+4\right)}$$

Short Solution Steps

Divide \frac{c^{2}+3c+2}{c^{2}+7c+12} by \frac{c^{2}-1}{c^{2}-9} by multiplying \frac{c^{2}+3c+2}{c^{2}+7c+12} by the reciprocal of \frac{c^{2}-1}{c^{2}-9}.

$$\frac{\left(c^{2}+3c+2\right)\left(c^{2}-9\right)}{\left(c^{2}+7c+12\right)\left(c^{2}-1\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(c-3\right)\left(c+1\right)\left(c+2\right)\left(c+3\right)}{\left(c-1\right)\left(c+1\right)\left(c+3\right)\left(c+4\right)}$$

Cancel out \left(c+1\right)\left(c+3\right) in both numerator and denominator.

$$\frac{\left(c-3\right)\left(c+2\right)}{\left(c-1\right)\left(c+4\right)}$$

Expand the expression.

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

Expand

$$\frac{c^{2}-c-6}{\left(c-1\right)\left(c+4\right)}$$

Short Solution Steps

Divide \frac{c^{2}+3c+2}{c^{2}+7c+12} by \frac{c^{2}-1}{c^{2}-9} by multiplying \frac{c^{2}+3c+2}{c^{2}+7c+12} by the reciprocal of \frac{c^{2}-1}{c^{2}-9}.

$$\frac{\left(c^{2}+3c+2\right)\left(c^{2}-9\right)}{\left(c^{2}+7c+12\right)\left(c^{2}-1\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(c-3\right)\left(c+1\right)\left(c+2\right)\left(c+3\right)}{\left(c-1\right)\left(c+1\right)\left(c+3\right)\left(c+4\right)}$$

Cancel out \left(c+1\right)\left(c+3\right) in both numerator and denominator.

$$\frac{\left(c-3\right)\left(c+2\right)}{\left(c-1\right)\left(c+4\right)}$$

Expand the expression.

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