Rationalizing the numerator with limits

1. May 21, 2012

robertjford80

1. The problem statement, all variables and given/known data

3. The attempt at a solution

I don't see how the above step is legal. I plugged in 4 for z and 9 for z and it works, but what is this move called? it's neither rationalizing the numerator nor rationalizing the denominator.

2. May 22, 2012

Dick

It's called factoring. z-x=(sqrt(z)-sqrt(x))*(sqrt(z)+sqrt(x)). It should work ok as long as z and x are nonnegative. I think you can assume that because otherwise your numerator isn't very well defined.

3. May 22, 2012

e^(i Pi)+1=0

FOIL the denominator in the second step and you'll get back what you started with.