Please solve the last limet written down below ${[}_{-}^0|]$

vec$(H)=\frac{-Ivec(a{)}_{}}{4}\underset{-}{lim}(\frac{z}{e^2\sqrt[\phantom{2}]{e^2+(z{)}^2}}-\frac{z-L}{e^2\sqrt[\phantom{2}]{e^2+(z-L{)}^2}})$