# How do you add or subtract (5y)/(1-4y^2 ) - ( 2y)/(2y+1) + (5y)/(4y^2-1)?

First, notice that $4 {y}^{2} - 1$ = -(1-4y^2),
then rewrite $\frac{5 y}{4 {y}^{2} - 1}$ as $- \frac{5 y}{1 - 4 {y}^{2}}$,
which allows you to get rid of the first $\frac{5 y}{1 - 4 {y}^{2}}$ term
and you are left with only $- \frac{2 y}{2 y + 1}$.