SOLUTION: This seems like a simple problem... however, I'm trying to learn the core reason on how and why this problem works. (I got the answer from the back of my math book, but I want to u

Algebra ->  Radicals -> SOLUTION: This seems like a simple problem... however, I'm trying to learn the core reason on how and why this problem works. (I got the answer from the back of my math book, but I want to u      Log On


   

Question 26578: This seems like a simple problem... however, I'm trying to learn the core reason on how and why this problem works. (I got the answer from the back of my math book, but I want to understand it.)
b-a^(-1) / a-b^(-1)
Thanks.
Answer by longjonsilver(2297) About Me  (Show Source):
You can put this solution on YOUR website!
you do not say whether your powers apply to all the terms or just the second in each pair?

%28x%29%5E%28-2%29 is 1/(x)^2

so, %28b-a%29%5E-1%29 is 1/(b-a)
Similarly %28a-b%29%5E-1%29 is 1/(a-b)

so %28b-a%29%5E%28-1%29%2F%28a-b%29%5E%28-1%29 becomes %281%2F%28b-a%29%29%2F%281%2F%28a-b%29%29 which is
%28a-b%29%2F%28b-a%29

jon.