Uniform convergence of $f_n(x) = \frac{\ln(1+\frac{x}{n})}{x+1}$ [duplicate]

Basically i have a problem proving the sequence in the title 1. Uniformly converges on a closed interval $[0,a]$ where $a > 0$ and 2. Uniformly converges on $[0,\infty).$ So far i have found the limit it converges to pointwise, its pretty clear it goes to 0. Then i tried the uniform convergence on [0,a], but i cannot find anything that i could use with the Weierstrass theorem. Then i tried the other way, of calculating the supremum of $|f_n(x) - f(x)| = |f_n(x)|$, but after calculating the derivative it appears to me as though the derivative doesnt have a zero. So what could i try next. I know that for a fact it is uniformly convergent or at least thats what the solution says so i didnt try to prove it isnt, i just dont know how to proceed