CPM Homework Help : PCT Problem 9-131

Show that: $\frac { \sqrt { 3 ( x + h ) } - \sqrt { 3 x } } { h } = \frac { \sqrt { 3 } } { \sqrt { x + h } + \sqrt { x } }$ by rationalizing the numerator and simplifying.

Hint:

Multiply both the numerator and denominator by the conjugate.

More help:

$\left( \frac{\sqrt{3(x+h)}-\sqrt{3x}}{h} \right) \left( \frac{\sqrt{3(x+h)}+\sqrt{3x}}{\sqrt{3(x+h)}+\sqrt{3x}} \right)$

Answer:

$\frac{\sqrt{3}}{\sqrt{x+h}+\sqrt{x}}$