Lim x approaches infinity of (square root of x^2 +2)/ x-1

The answer is 
lim sqrt (x^2 +2) /x - 1 = lim sqrt [x^2(1 +2 / x^2) /x - 1 =
lim   x sqrt [(1 +2 / x^2) / x(1 - 1/x)= lim  sqrt [(1 +2 / x^2) / (1 - 1/x)
and when x approaches infinity we have 
lim sqrt (x^2 +2) /x - 1 = sqrt [(1 +0 ) / (1 - 0) = 1/1 = 1