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

1 Answer
May 28, 2016

Answer:

#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.