Simple Precalculus: Average rate of change

DarrenM

1. The problem statement, all variables and given/known data
Find the average rate of change:
g(x)=1/x; x = 1, x = a


2. Relevant equations
(f(b)-f(a))/(b-a) = Average rate of change


3. The attempt at a solution
I've spent far too much time on this problem, but I know I'm making a stupid error and I just can't pin it down. So far, the steps I'm pretty confident about:

g(1) = 1/1 = 1
g(a) = 1/a

Average rate of change = ((1/a)-1)/(a-1)

According to the book the answer is -(1/a)... but I'm just not seeing it.

rock.freak667

1/a-1 = (1-a)/a

DarrenM

Yea, got it now. It was just as ridiculous an oversight as I had originally thought. I kept getting to the point in the problem where I had (1-a)/(a(a-1)) and going, "Oh, I can't divide those binomials!" Factor out a -1 from the numerator, cancel out the resulting binomial with the denominator and there's the answer... staring me right in the face. I'm rather embarrassed that I had so much trouble with such a simple problem, and that I forgot such a basic rule. Thanks for the help.