Rationalize the denominator. Assume that all variables represent nonnegative numbers and that the denominator is not
zero.
-$\frac { 4 } { \sqrt { x + h } - \sqrt { x } }$
A) $\frac { 4 ( \sqrt { x + h } - \sqrt { x } ) } { h }$
B) $\frac { 4 \sqrt { h } } { h }$
C) $\frac { 4 \sqrt { x + h } + \sqrt { x } } { h }$
D) $\frac { 4 ( \sqrt { x + h } + \sqrt { x } ) } { h }$

Question

Quizplus · Accepted Answer

To rationalize the denominator, multiply the numerator and denominator by the conjugate of the denominator, which is $\sqrt{x + h} + \sqrt{x}$. This results in $\frac{4(\sqrt{x + h} + \sqrt{x})}{(\sqrt{x + h} - \sqrt{x})(\sqrt{x + h} + \sqrt{x})} = \frac{4(\sqrt{x + h} + \sqrt{x})}{h}$, simplifying to choice D.

Rationalize the Denominator 4x+h−x\frac { 4 } { \sqrt { x + h } - \sqrt { x } }x+h​−x​4​

Rationalize the Denominator $\frac { 4 } { \sqrt { x + h } - \sqrt { x } }$