Define g: (0,1)\to\mathbb{R} by g (x)=\frac{\sqrt{1+x}-1}{x}. Prove that g has a limit at 0 and find it.

In my course we are given only the definition of a limit, namely that g has a limit at x_0 iff there exists a \delta such that given any \epsilon >0 we have

|g(x)-L|<\epsilon for all 0<|x-x_0|<\delta.

We are also given the algebra of limits for Addition, Multiplication, and Division (given obvious constraints).

I cannot seem to find a clever way to write g(x) in the problem as a composition of two functions with either of these three operations. Any help would be appreciated.