I tired using the L'Hospitale's rule, but it didn't help. The damned "x" won't go away!Then I tired to rewrite it as
1/sqrt(x+a)-1/sqrt x) = (sqrt x- sqrt(x+a) )/sqrt(x(x+a))
and tried multiplying both the numerator and the denominator with (sqrt x + sqrt (x+a) ).That didn't work either...