Calculus Help! lim x -->√2 [ (1/ √2) - (1/x)]/ (√2) - x

answer = -1/2, just need to know how to do the steps.

thanks in advance!!

lim x -->√2, [ (1/ √2) - (1/x)]/ (√2) - x)

multiply top and bottom with -1

=> lim x -->√2, - [ (1/ √2) - (1/x)]/( x - √2)

take common denominator for the two terms of the numerator

=> lim x -->√2, - [ x - √2) ]/√2 x( x - √2)

cancel x - √2

=> lim x -->√2, [ -1 /(√2 x) ]

= -1/√(√2 √2)

= -1/2