Expert: Bobby Soltani - 1/8/2006

Question
Simplify.

r - 5     r² - 25
------ * ------
r + 5     5 - r


I don't know what to do here.

Can you help me?

Answer
Hi Emma,

You first need to recognize that r^2-25 is in the form a^2 - b^2, where a = r, and b = 5.  When you have something like this you can use the property

a^2 - b^2 = (a+b)(a-b)

So, we can write

((r - 5)*(r + 5)(r - 5)) / ((r + 5)(5 - r))

now the r+5 in the numerator cancels with the r+5 in the denominator.

((r - 5)*(r - 5)) / (5 - r)

if we multiply the top and the bottom by -1, we get

(-(r - 5)*(r - 5) / (r - 5)

the bottom works out that way because -(5 - r) = -5 + r = r - 5

now, one of the r - 5 on the top cancels with the r - 5 on the bottom.

= -(r - 5)
or
= 5 - r

Let me know if you have any questions.

Bobby