Rationalizing the numerator with limits

[robertjford80]

Homework Statement

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.

 

[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.

 

[e^(i Pi)+1=0]

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