Question

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

Answer 1

`1/(x(1-sqrtx))=(1+sqrtx)/(x(1-x))`

Explanation:

To rationalize the denominator and simplify `1/(x(1-sqrtx))`, one needs to multiply the numerator and denominator, by the conjugate of `(1-sqrtx)`, i.e. by `(1+sqrtx)`.

Hence,

`1/(x(1-sqrtx))=(1+sqrtx)/(x(1-sqrtx)(1+sqrtx))`

= `(1+sqrtx)/(x(1-x))`

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