To simplify the expression, we first need to combine like terms.

The expression given is:
(3y + 2)/(4y^2 + y) + y - 3/(16y^2 - 1) = 3/(4y - 1)

Combining like terms, we get:
(3y + 2)/(4y^2 + y) + y - 3/(16y^2 - 1) = 3/(4y - 1)
(3y + 2)/(4y^2 + y) + y - 3/(4y + 1)(4y - 1) = 3/(4y - 1)

Now, to further simplify this expression, we can find a common denominator for all the terms.

The common denominator would be:
(4y^2 + y)(4y - 1)

Multiplying all terms by the common denominator, we get:
(3y + 2)(4y - 1) + y(4y^2 + y) - 3 = 3(4y^2 + y)

Expanding both sides:
12y^2 - 3y + 8y - 2 + 4y^3 + y^2 - 3 = 12y^2 + 3y

Combining like terms:
4y^3 + 13y^2 + 5y - 5 = 12y^2 + 3y

Rearranging the terms:
4y^3 + 13y^2 + 5y - 5 - 12y^2 - 3y = 0
4y^3 + y^2 + 2y - 5 = 0

So, the simplified expression is:
4y^3 + y^2 + 2y - 5 = 0