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

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) $\frac { 4 \sqrt { x + h } + \sqrt { x } } { h }$

Quizplus · Accepted Answer

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

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

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