limits - Find $limlimits_{nrightarrow infty} nlnleft(1+frac{x}{sqrt{n}}right)-xsqrt{n}$

As the title suggests, I need to prove the

$$\lim_{n\rightarrow \infty} n\ln\left(1+\frac{x}{\sqrt{n}}\right)-x\sqrt{n} = \frac{-x^2}{2}$$ I've tried to used things like L'hospitals but to no avail. Any ideas?