Question

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

Answer 1

First, notice that `4y^2-1` = `-(1-4y^2`),

then rewrite `(5y)/(4y^2-1)` as `-(5y)/(1-4y^2)`,

which allows you to get rid of the first `(5y)/(1-4y^2)` term
and you are left with only `-(2y)/(2y+1)`.