19. $$ \frac{r^{2}+5 r+6}{2 r} \cdot \frac{r-2}{r+3} $$

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Calculate or simplify the expression $$ (r^{2}+5r+6)/(2r) * (r-2)/(r+3) $$.
Simplify the expression by following steps:
- step0: Solution:
  $$\frac{\frac{\left(r^{2}+5r+6ight)}{2r}	imes \left(r-2ight)}{\left(r+3ight)}$$
- step1: Remove the parentheses:
  $$\frac{\frac{r^{2}+5r+6}{2r}	imes \left(r-2ight)}{r+3}$$
- step2: Multiply the terms:
  $$\frac{\frac{\left(r^{2}+5r+6ight)\left(r-2ight)}{2r}}{r+3}$$
- step3: Multiply by the reciprocal:
  $$\frac{\left(r^{2}+5r+6ight)\left(r-2ight)}{2r}	imes \frac{1}{r+3}$$
- step4: Rewrite the expression:
  $$\frac{\left(r+3ight)\left(r+2ight)\left(r-2ight)}{2r}	imes \frac{1}{r+3}$$
- step5: Reduce the fraction:
  $$\frac{\left(r+2ight)\left(r-2ight)}{2r}	imes 1$$
- step6: Multiply the terms:
  $$\frac{\left(r+2ight)\left(r-2ight)}{2r}$$
- step7: Multiply the terms:
  $$\frac{r^{2}-4}{2r}$$
The simplified form of the expression $$ \frac{r^{2}+5r+6}{2r} \cdot \frac{r-2}{r+3} $$ is $$ \frac{r^{2}-4}{2r} $$.
The simplified form of the expression is $$ \frac{r^{2}-4}{2r} $$.

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