Uniform convergence for $\frac{x^2+nx+1}{x+n}$ in $\mathbb{R}_+$

Question

I have this problem: Prove that $ f_n:\mathbb{R}_+\rightarrow \mathbb{R}$ $$f_n(x)=\frac{x^2+nx+1}{x+n}$$ converges uniformly to $f(x)=x$. I did this: $$|f_n(x)-f(x)| <\epsilon$$$$ \left|\frac{x^2+nx+1}{x+n} -x \right| <\epsilon$$ $$\left|\frac{1}{x+n} \right| \le \frac{1}{n} < \epsilon, n> \frac{1}{\epsilon}$$ What I have to do now?