1/4(y+b)+1/4(y-b)+y/2(y^2-b^2)-y^3/y^4-b^4

Answer 1

That is equal to

(-2b^4y - b^2y^2 + y^2 + y^4 - 2)/(2y)

I suspect you mean

1/(4(y+b))+1/(4(y-b))+y/(2(y^2-b^2))-y^3/(y^4-b^4) = (b^2y)/(y^4-b^4)

parentheses can make a huge difference. Use them.

Answer 2

b^2y/(y^4-b^4)