Simplify each term.

Simplify the denominator.

Rewrite as .

Since both terms are perfect squares, factor using the difference of squares formula, where and .

Simplify the denominator.

Rewrite as .

Since both terms are perfect squares, factor using the difference of squares formula, where and .

Combine the numerators over the common denominator.

Rewrite as .

Check the middle term by multiplying and compare this result with the middle term in the original expression.

Simplify.

Factor using the perfect square trinomial rule , where and .

Factor out of .

Cancel the common factors.

Cancel the common factor.

Rewrite the expression.

Simplify (y^2)/(y^2-1)+(2y+1)/(y^2-1)