# How do you simplify the expression ((r^2-9r)/(r^2+7r+10))/((r^2+5r)/(r^2+r-2))?

Apr 10, 2017

$\frac{\left(r - 9\right)}{\left(r + 5\right)} \cdot \frac{\left(r - 1\right)}{\left(r + 5\right)}$

#### Explanation:

((r(r-9))/((r+5)(r+2)))/((r(r+5))/((r-1)(r+2))

$\frac{r \left(r - 9\right)}{\left(r + 5\right) \left(r + 2\right)} \cdot \frac{\left(r - 1\right) \left(r + 2\right)}{r \left(r + 5\right)}$

$\frac{\left(r - 9\right)}{\left(r + 5\right)} \cdot \frac{\left(r - 1\right)}{\left(r + 5\right)}$

If you want you can multiply this .. it's your turn

Apr 10, 2017

color(red)(((r-9)(r-1))/((r+5)(r+5))

#### Explanation:

((r^2-9r)/(r^2+7r+10))/((r^2+5r)/(r^2+r-2)

$\therefore = \left(\frac{{r}^{2} - 9 r}{1} \times \frac{1}{{r}^{2} + 7 r + 10}\right) \div \left(\frac{{r}^{2} + 5 r}{1} \times \frac{1}{{r}^{2} + r - 2}\right)$

$\therefore = \frac{r \left(r - 9\right)}{\left(r + 2\right) \left(r + 5\right)} \div \frac{r \left(r + 5\right)}{\left(r - 1\right) \left(r + 2\right)}$

$\therefore = \frac{r \left(r - 9\right)}{\cancel{\left(r + 2\right)} \left(r + 5\right)} \times \frac{\left(r - 1\right) \cancel{\left(r + 2\right)}}{r \left(r + 5\right)}$

:.=(cancelr(r-9))/(r+5) xx ((r-1))/(cancelr(r+5)

:.=color(red)(((r-9)(r-1))/((r+5)(r+5))