Rationalize the numerator of the expression and simplify.
-$$\frac { \sqrt { 3 ( x + h ) } - \sqrt { 3 x } } { h }$$
A) $\frac { 3 } { \sqrt { 3 x + 3 h } + \sqrt { 3 x } }$
B) $\frac { 6 x + 3 h } { h \sqrt { 3 x + 3 h } + \sqrt { 3 x } }$
C) $\frac { 3 h } { \sqrt { 3 x + 3 h } + \sqrt { 3 x } }$
D) $\frac { 3 } { \sqrt { 6 x + 3 h } }$

Question

Quizplus · Accepted Answer

To rationalize the numerator, multiply the given expression by the conjugate of the numerator over itself: $\frac{\sqrt{3(x+h)} - \sqrt{3x}}{h} \cdot \frac{\sqrt{3(x+h)} + \sqrt{3x}}{\sqrt{3(x+h)} + \sqrt{3x}}$. This simplifies to $\frac{3(x+h) - 3x}{h(\sqrt{3(x+h)} + \sqrt{3x})}$, which further simplifies to $\frac{3h}{h(\sqrt{3(x+h)} + \sqrt{3x})}$, resulting in $\frac{3}{\sqrt{3(x+h)} + \sqrt{3x}}$, matching choice A.

Rationalize the Numerator of the Expression and Simplify 3(x+h)−3xh\frac { \sqrt { 3 ( x + h ) } - \sqrt { 3 x } } { h }h3(x+h)​−3x​​

Rationalize the Numerator of the Expression and Simplify $\frac { \sqrt { 3 ( x + h ) } - \sqrt { 3 x } } { h }$