# How do you rationalize the denominator and simplify 1/ (x(1-sqrt x) ) ?

May 28, 2016

$\frac{1}{x \left(1 - \sqrt{x}\right)} = \frac{1 + \sqrt{x}}{x \left(1 - x\right)}$

#### Explanation:

To rationalize the denominator and simplify $\frac{1}{x \left(1 - \sqrt{x}\right)}$, one needs to multiply the numerator and denominator, by the conjugate of $\left(1 - \sqrt{x}\right)$, i.e. by $\left(1 + \sqrt{x}\right)$.

Hence,

$\frac{1}{x \left(1 - \sqrt{x}\right)} = \frac{1 + \sqrt{x}}{x \left(1 - \sqrt{x}\right) \left(1 + \sqrt{x}\right)}$

= $\frac{1 + \sqrt{x}}{x \left(1 - x\right)}$

Note here we have avoided $x$, as it is a rational expression.