quantum mechanics - Prove that angular momentum commute with the hamiltonian of a central force

I'm trying to prove that

$$[\hat{L}_i,\hat{H}]=0$$ for $\hat{H}$ the hamiltonian of a central force $$\hat{H}=\frac{\hat{p}^2}{2m}-\frac{\alpha}{r}.$$

I'm getting this:

$$[\hat{L}_i,\hat{H}]=[\hat{L}_i,\frac{\hat{p}^2}{2m}-\frac{\alpha}{r}] = [\hat{L}_i , \frac{\hat{p}^2}{2m}] - [\hat{L}_i , \frac{\alpha}{r}].$$

Already prove that the first one is zero (it's a known result too), but the second one, I dont know what to do with it, there is no way for me. I was doing something like this:

$$[\hat{L}_i , \frac{\alpha}{r}] = [\epsilon_{ijk} r_j p_k , \frac{\alpha}{r}] = \epsilon_{ijk}r_j [p_k ,\frac{\alpha}{r}] + \epsilon_{ijk} [r_j , \frac{\alpha}{r}]p_k.$$

Obviously, the last term is zero, but the other one, I do something that has no sense to be zero. Have any idea for this? I'm I doing wrong? All of this is to prove that Laplace-Runge-Lenz operator commute with hamiltonian of a central force.