Finding a limit at g(x). Analysis. Algebra of Limits.

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.