# How do you simplify (3m^2 + 9m + 6) / (4m^2 + 12m + 8)?

Jul 4, 2015

#### Answer:

$\frac{3 {m}^{2} + 9 m + 6}{4 {m}^{2} + 12 m + 8} = \frac{3}{4}$

with exclusions $m \ne - 1$ and $m \ne - 2$

#### Explanation:

$\frac{3 {m}^{2} + 9 m + 6}{4 {m}^{2} + 12 m + 8}$

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

$= \frac{3}{4} \cdot \frac{{m}^{2} + 3 m + 2}{{m}^{2} + 3 m + 2}$

$= \frac{3}{4}$

However, it is possible for ${m}^{2} + 3 m + 2 = 0$.

${m}^{2} + 3 m + 2 = \left(m + 1\right) \left(m + 2\right)$

which is zero when $m = - 1$ or $m = - 2$.

For these values of $m$ the original rational expression is not defined.