doubt in working with roots

[ohwell]

If x > 0, then 1/[√(2x)+√x] =

A. 1/√(3x)
B. 1/[2√(2x)]
C. 1/(x√2)
D. (√2-1)/√x
E. (1+√2)/√x

Correct answer = D

Could someone please show step by step how to get to this answer?

Thanks

[cramya]

Mutliply and divide by sqrt(2x) - sqrt(x)

sqrt(2*x) - sqrt(x) / 2x-x

sqrt(2) sqrt(x) - sqrt(x) / x

= sqrt(x) (sqrt(2) - 1) / x

=sqrt(2) - 1 / sqrt(x)

D)

[ohwell]

Thanks cramya. You make it look easy.