Question

Simplify the expression$\frac{r^2+2r-8}{r^2+4r+3}÷\frac{r-2}{3r+3}$

Short answer

The simplified value of expression is $\frac{3\left(r+4\right)}{\left(r+3\right)}$.

Step-by-step solution

Step 1. Write down the given expression.

The given expression is$\frac{r^2+2r-8}{r^2+4r+3}÷\frac{r-2}{3r+3}$

Step 2. Simplify the expression.

The given expression $\frac{r^2+2r-8}{r^2+4r+3}÷\frac{r-2}{3r+3}$is simplified as:

$\begin{array}{c}\frac{r^2+2r-8}{r^2+4r+3}÷\frac{r-2}{3r+3}=\frac{r^2+2r-8}{r^2+4r+3}\times \frac{3r+3}{r-2}\\ =\frac{\left(r+4\right)\left(r-2\right)}{\left(r+3\right)\left(r+1\right)}\times \frac{3\left(r+1\right)}{r-2}\\ =\frac{3\left(r+4\right)}{\left(r+3\right)}\end{array}$

Step 3. Conclusion.

The simplified value of expression is $\frac{3\left(r+4\right)}{\left(r+3\right)}$.