How do you simplify the expression $\frac{\frac{r^{2} - 9 r}{r^{2} + 7 r + 10}}{\frac{r^{2} + 5 r}{r^{2} + r - 2}}$ $((r^2-9r)/(r^2+7r+10))/((r^2+5r)/(r^2+r-2))$ ?

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Answer 1 · 2017-04-10T18:56:05

$\frac{(r - 9)}{(r + 5)} \cdot \frac{(r - 1)}{(r + 5)}$ $((r-9))/((r+5))*((r-1))/((r+5))$

$\frac{\frac{r (r - 9)}{(r + 5) (r + 2)}}{\frac{r (r + 5)}{(r - 1) (r + 2)}}$ $((r(r-9))/((r+5)(r+2)))/((r(r+5))/((r-1)(r+2))$

$\frac{r (r - 9)}{(r + 5) (r + 2)} \cdot \frac{(r - 1) (r + 2)}{r (r + 5)}$ $(r(r-9))/((r+5)(r+2))*((r-1)(r+2))/(r(r+5))$

$\frac{(r - 9)}{(r + 5)} \cdot \frac{(r - 1)}{(r + 5)}$ $((r-9))/((r+5))*((r-1))/((r+5))$

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

Answer 2 · 2017-04-10T19:31:47

$\frac{(r - 9) (r - 1)}{(r + 5) (r + 5)}$ $color(red)(((r-9)(r-1))/((r+5)(r+5))$

$\frac{\frac{r^{2} - 9 r}{r^{2} + 7 r + 10}}{\frac{r^{2} + 5 r}{r^{2} + r - 2}}$ $((r^2-9r)/(r^2+7r+10))/((r^2+5r)/(r^2+r-2)$

$:.=((r^2-9r)/1 xx 1/(r^2+7r+10))-:((r^2+5r)/1 xx 1/(r^2+r-2))$

$:.=(r(r-9))/((r+2)(r+5))-:(r(r+5))/((r-1)(r+2))$

$:.=(r(r-9))/(cancel((r+2))(r+5)) xx ((r-1)cancel((r+2)))/(r(r+5))$

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

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

How do you simplify the expression ((r^2-9r)/(r^2+7r+10))/((r^2+5r)/(r^2+r-2))r2−9rr2+7r+10r2+5rr2+r−2((r^2-9r)/(r^2+7r+10))/((r^2+5r)/(r^2+r-2))?