Chapter 11.2, Problem 19PPE

To determine

Multiply: $\frac{r^2+5r+6}{2r}·\frac{r-2}{r+3}$

Answer to Problem 19PPE

  $\frac{r^2+5r+6}{2r}·\frac{r-2}{r+3}=\frac{r^2-4}{2r}$

Explanation of Solution

Given:

Multiply: $\frac{r^2+5r+6}{2r}·\frac{r-2}{r+3}$

Concept Used:

For multiplication of rational expression, we always cancel the common factor from numerator and denominator and if necessary multiply the numerators and denominators separately.

Calculation:

  $\begin{array}{l}\frac{r^2+5r+6}{2r}·\frac{r-2}{r+3}\\ \frac{(r+3)(r+2)}{2r}·\frac{(r-2)}{(r+3)}=\frac{(r+3)}{(r+3)}·\frac{(r+2)(r-2)}{2r}\\ \frac{(r+2)(r-2)}{2r}=\frac{r^2-4}{2r}\end{array}$

Thus, $\frac{r^2+5r+6}{2r}·\frac{r-2}{r+3}=\frac{r^2-4}{2r}$