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 - 80 = 18y^2 - 23y - 70 = (3y - 7)(6y + 1)
Setting each factor to zero and solve for y:
3y - 7 = 03y = 7y = 7/3
6y + 1 = 06y = -1y = -1/6
Therefore, the solutions to the equation are y = 7/3 and y = -1/6.
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.