To rationalize the numerator of the expression \(\frac{2\sqrt{x} + h - 2\sqrt{x}}{h}\), we can first simplify the expression. The terms \(2\sqrt{x}\) and \(-2\sqrt{x}\) will cancel each other out.
So, we rewrite the expression:
\[ \frac{(2\sqrt{x} + h) - 2\sqrt{x}}{h} = \frac{h}{h} = 1 \]
Thus, the given expression simplifies to:
\[ 1 \]
If the goal is to rationalize the numerator of a more general form, such as \(\frac{2\sqrt{x} + h}{h} - \frac{2\sqrt{x}}{h}\), we apply the multiplication of a conjugate. However, in your case, since \(2\sqrt{x} - 2\sqrt{x} = 0\), we have reached a finished form.
If there's a specific alternative expression you want to work with or if there are other details you have in mind regarding rationalization, please provide that, and I can assist further!
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