prove the following equivalence $\ln(-\frac{l-x+\sqrt{r^2+(l-x)}}{l+x-\sqrt{r^2+(l+x)}})={}$ArcSinh$(\frac{l+x}{r})+{}$ArcSinh$(\frac{l-x}{r})$

Question

Hi guys i'm trying to prove the following equivalence but i'm having some problems:

$$\ln\left(-\frac{\ell-x+\sqrt{r^2+(\ell-x)^{2}}}{\ell+x-\sqrt{r^2+(\ell+x)^{2}}}\right) = \operatorname{ArcSinh} \left(\frac{\ell+x}{r} \right) + \operatorname{ArcSinh} \left(\frac{\ell-x}{r}\right)$$

here all the parameters $\ell$, $x$ and $r$ are real numbers and $\operatorname{ArcSinh}$ is the inverse hyperbolic Sin function.

remind that $\operatorname{ArcSinh}(x)=\ln\left(x+\sqrt{1+x^2}\right)$

thanks in advance.