Для начала приведем дроби к общему знаменателю:

5y/(y-1) + 7y/[2(y+1)] = (5y2(y+1) + 7y(y-1))/[2(y+1)(y-1)]

Упростим числитель:

= (10y^2 + 10y + 7y^2 - 7y)/[2(y+1)(y-1)]
= (17y^2 + 3y)/[2(y+1)(y-1)]
= (y(17y + 3))/[2(y+1)(y-1)]
= y(17y + 3)/[2y(y+1)(y-1)]
= (17y + 3)/[2(y+1)(y-1)].

Таким образом, результатом сложения 5y/(y-1) + 7y/[2(y+1)] будет (17y + 3)/[2(y+1)(y-1)].