# How do you find the quotient of (r+2)/(r+1)div4/(r^2+3r+2)?

Apr 8, 2017

$= {\left(r + 2\right)}^{2} / 4$

#### Explanation:

$\frac{r + 2}{r + 1} \div \frac{4}{{r}^{2} + 3 r + 2}$

change a sign $\div$ to * (multiplication) and the location of $\frac{4}{{r}^{2} + 3 r + 2}$

$= \frac{r + 2}{r + 1} \cdot \frac{{r}^{2} + 3 r + 2}{4}$

factorize $\left({r}^{2} + 3 r + 2\right)$

$= \frac{r + 2}{\cancel{r + 1}} \cdot \frac{\left(r + 2\right) \cancel{\left(r + 1\right)}}{4}$

$= {\left(r + 2\right)}^{2} / 4$