3y-3/3y-2+6+2y/3y+2=2

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To solve this equation, we need to combine like terms and simplify both sides.

Starting with the left side of the equation:

3y - 3 / 3y - 2 + 6 + 2y / 3y + 2
= (3y - 3) / (3y - 2) + 6 + (2y) / (3y + 2)
= (3y - 3 + 6(3y - 2) + 2y) / (3y - 2)(3y + 2)
= (3y - 3 + 18y - 12 + 2y) / (9y^2 - 4)
= (23y - 15) / (9y^2 - 4)

Now simplifying the right side of the equation, which is already simplified to 2:

2

Putting both sides together:

(23y - 15) / (9y^2 - 4) = 2

Now we can cross multiply to solve for y:

23y - 15 = 2(9y^2 - 4)
23y - 15 = 18y^2 - 8
0 = 18y^2 - 23y - 7
0 = (3y - 7)(6y + 1)

Setting each factor to zero and solve for y:

3y - 7 = 0
3y = 7
y = 7/3

6y + 1 = 0
6y = -1
y = -1/6

Therefore, the solutions to the equation are y = 7/3 and y = -1/6.