Looking for the limit of a function g(x). Algebra of Limits problem. Analysis 4420

Define $\displaystyle g: (0,1)\to\mathbb{R} $ by $\displaystyle g (x)=\frac{\sqrt{1+x}-1}{x}$. 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 $\displaystyle g$ has a limit at $\displaystyle x_0$ iff there exists a $\displaystyle \delta$ such that given any $\displaystyle \epsilon >0$ we have

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

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.