Write as a sum of fractions 1/y(y+1)

We remark that the denominator of the given ratio is the
least common denominator of 2 irreducible ratios.

The
final ratio 1/y(y+1) is the result of addition or subtraction of 2 elementary fractions,
as it follows:

1/y(y+1) = A/y + B/(y+1)
(1)

We'll multiply by y(y+1) both
sides:

1 = A(y+1) + By

We'll
remove the brackets:

1 = Ay + A +
By

We'll factorize by y to the right
side:

1 = y(A+B) + A

We'll
compare expressions of both sides:

A+B =
0

A = 1

1 + B =
0

B = -1

We'll substitute A
and B into the expression (1) and we'll get the algebraic sum of 2 elementary
fractions:

1/y(y+1) = 1/y -
1/(y+1)