Simplifying Limit Expressions with Rationalization: f(x) = √(x-1)

[Jamin2112]

Homework Statement

Fore each of the following functions, find the expression for [ f(x+h) - f(x)] / h. Simplify each of your expressions far enough so that plugging in h=0 would be allowed.

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(f). f(x) = √(x-1) (Hint: Rationalize the numerator)

Homework Equations

Nothing, really.

The Attempt at a Solution

So a friend of mine asked me this question and I couldn't really figure it out. If you can, show me the simplification process.

I can get it to (x+h-1)/(h√(x+h-1)) - (x-1)/(h√(x-1))

 

[ideasrule]

That's not how you're supposed to rationalize the numerator. Write out the limit as one fraction, and rationalize the entire numerator: sqrt(x-1+h) - sqrt(x-1). The purpose of this will become clear once you get the answer.