find (gof)(x) when f(x) = √x+1 and g(x) = x^2+3/x

Using what you typed (rather than what you might have meant),

g(x) = x^2 + 3/x, so
(g◦f)(x) = g(f) = f^2 + 3/f
= (√x + 1)^2 + 3/(√x + 1)
= x + 2√x + 1 + 3/(√x + 1)

If you need some parentheses, add 'em in and revise the answer.