How Do You Simplify the Limit of f(x)=√x at x=7?

[3.141592654]

Homework Statement

Use this limit for the following problems: lim as h approaches 0 of [f(x+h)-f(x)]/h.

f(x)=\sqrt{x}, x=7

Homework Equations

The Attempt at a Solution

lim as h approaches 0 of [f(x+h)-f(x)]/h

= lim as h approaches 0 of (\sqrt{7+h}-\sqrt{7})/h

I'm having trouble simplifying the numerator, is there any way to get rid of the square roots in the numerator? Thank you.

 

[Office_Shredder]

Rationalize the numerator

\frac{ (\sqrt{7+h} - \sqrt{7})( \sqrt{7+h} + \sqrt{7})}{h( \sqrt{7+h} + \sqrt{7}}