# How do you simplify (c^2+c-56)/(c^2+10c+16)?

Oct 18, 2015

Factor each of the quadratics and eliminate the common factors to find:

$\frac{{c}^{2} + c - 56}{{c}^{2} + 10 c + 16} = \frac{c - 7}{c + 2} = 1 - \frac{9}{c + 2}$

with restriction $c \ne - 8$

#### Explanation:

$\frac{{c}^{2} + c - 56}{{c}^{2} + 10 c + 16} = \frac{\left(c + 8\right) \left(c - 7\right)}{\left(c + 8\right) \left(c + 2\right)} = \frac{c - 7}{c + 2}$

with restriction $c \ne - 8$

The restriction is necessary, because if $c = - 8$ then both the numerator and denominator of the original expression are $0$ so their quotient is undefined, but the simplified expression $\frac{c - 7}{c + 2}$ is defined when $c = - 8$.

Also

$\frac{c - 7}{c + 2} = \frac{c + 2 - 2 - 7}{c + 2} = 1 - \frac{9}{c + 2}$