Question

Divide r+5/ r^2+5r-14 by r^2+4-21/r-2

Answer 1

So we want to divide
`(r+5)/(r^2+5r-14)` by
`(r^2+4r-21)/(r-2)`.
The first thing we are going to do is factor the denominator of the first fraction and the denominator of the second one:
- For our first fraction:

`r^2+5r-14=(r+7)(r-2)`
Now we can rewrite our first fraction:

`(r+5)/(r^2+5r-14) = (r+5)/((r+7)(r-2))`
- For our second fraction:

`r^2+4r-21=(r+7)(r-3)`
Now we can rewrite our second fraction:

`(r^2+4r-21)/(r-2) = ((r+7)(r-3))/(r-2)`

Last but not least, we can express our division as a fraction and simplify:

`((r+5)/((r+7)(r-2)))/( ((r+7)(r-3))/(r-2)) = ((r+5)(r-2))/((r+7)(r-2)(r+7)(r-3)) = (r+5)/((r+7)^2(r-3))`

We can conclude that the result of dividing r+5/ r^2+5r-14 by r^2+4r-21/r-2 is:
`(r+5)/((r+7)^2(r-3))`