(2/z-1) - 1/4 = 3/(z+1)
this is what you have asked for is it what you want?
$$\left({\frac{{\mathtt{2}}}{{\mathtt{z}}}}{\mathtt{\,-\,}}{\mathtt{1}}\right){\mathtt{\,-\,}}{\frac{{\mathtt{1}}}{{\mathtt{4}}}} = {\frac{{\mathtt{3}}}{\left({\mathtt{z}}{\mathtt{\,\small\textbf+\,}}{\mathtt{1}}\right)}}$$
anyway if it is firstly recognise that z cannot be 0 or -1
Simplify the LHS
then
multiply both sides by 4z(z+1)
that will get rid of all the fractions and make it easy to work with.
give it a go and if you get stuck or need more help then show us what you've done or ask us to help more.