Question

Rationalize the denominator- 12x/√x-10

Answer 1

ANSWER

$\frac{ - 12x \sqrt{x} - 120x}{ x - 100}$

EXPLANATION

The given function is

$\frac{ - 12x}{ \sqrt{x} - 10 }$

In the denominator we have

$\sqrt{x} - 10$

The conjugate of this surd is

$\sqrt{x} + 10$

To rationalize this function, we multiply both the numerator and the denominator by the conjugate surd.

$\frac{ - 12x (\sqrt{x} + 10)}{ (\sqrt{x} - 10)(\sqrt{x} + 1)}$

We apply the identity

$(a + b)(a - b) = {a}^{2} - {b}^{2}$

in the denominator.

This implies that,

$\frac{ - 12x (\sqrt{x} + 10)}{ (\sqrt{x})^{2} - {10}^{2} }$

$\frac{ - 12x \sqrt{x} - 120x}{ x - 100}$