Rationalize denominator?

Question

Hi.
Can someone please help me rationalize this denominator:
1/ x(1-sqrt x) ; 1 divided by x times ( 1 minus the square root of x).
Can you please show me step by step so I can learn the method.
Thank you!

Answer 1

1/x(1-√x) = 1/x-x√x * x+x√x / x+x√x
(multiply the numerator and the denominator by the conjugate of the denominator)
1/x-x√x * x+x√x / x+x√x = x+x√x / (x-x√x)(x+x√x)
= x+x√x / x^2 + x^2√x - x^2√x - x^3
= x+x√x / x^2 - x^3

that's the answer

Answer 2

1/ x(1-sqrt x)=?

multiply numerator and denominator by 1+sqrt(x)

{1+sqrt(x)} / {x(1-x)}

Answer 3

1/xx[1-sqrtx]=1/x[1-sqrt(x)]x[1+sqrt(x)]/[1+sqrt(x)]
=1+sqrt(x)/x[1-x].ANS.