How do you simplify (4c^2+12c+9)/(2c^2-11c-21)?

Aug 4, 2015

Factoring the numerator and denominator and then cancelling common terms gives:
$\textcolor{w h i t e}{\text{XXXX}}$$\frac{2 c + 3}{c - 7}$

Explanation:

$\frac{4 {c}^{2} + 12 c + 9}{2 {c}^{2} - 11 c - 21}$

$\textcolor{w h i t e}{\text{XXXX}}$$= \frac{\left(2 c + 3\right) \left(2 c + 3\right)}{\left(2 c + 3\right) \left(c - 7\right)}$

$\textcolor{w h i t e}{\text{XXXX}}$$= \frac{2 c + 3}{c - 7}$