Question

How do you evaluate `\frac { 3} { r + 9} - \frac { 1} { r - 9}`?

Answer 1

`(2(r-18))/((r+9)(r-9))`

Explanation:

First, you have to make both of them have the same denominator, and we usually do this by finding the "LCD," or Lowest Common Denominator. To make them both have LCDs, we must multiply the the entire first one by `(r-9)` and entire second by `(r + 9)`, so it looks like this:
`(3(r-9))/((r+9)(r-9)) - (r+9)/((r-9)(r+9))`

Now we simplify and solve:
`(3r-27)/((r+9)(r-9)) - (r+9)/((r-9)(r+9))` (distribute)

`((3r-27) - (r+9))/((r+9)(r-9))` (move all to one denominator)

`(3r-27-r-9)/((r+9)(r-9))` (distribute the "-")

`(2r-36)/((r+9)(r-9))` (combine like terms)

`(2(r-18))/((r+9)(r-9))` (factor out the 2)