limit

Apply the L-hospital rule to get Numerator as
12{(x-2)^-1/2+x^-1/2}(x²-4)^1/2
Denominator turns out to be x....
Thus limit comes out as 12.......if I've not done any calculation mistake....

also,cn separate the limits and write as;
1/√x+2 + √x-√2/√x²-4
now,multiply and divide √x+√2 in the 2nd limit,u'll get the 2nd limit 0.
thus limit=1/2 putting limits in the 1st one