You can put this solution on YOUR website! it's messy, but this is what i get and it checks out.
multiply both sides of the equation by y(y+2).
the equation is:
(1/y) + (1/(y+2) = 1/3
the equation becomes:
(y+2) + y = (y(y+2)/3
combine like terms and simplify to get:
2y + 2 = (y^2 + 2y)/3
multiply both sides by 3 to get:
6y + 6 = y^2 + 2y
subtract 6y + 6 from both sides of the equation to get:
0 = y^2 - 4y - 6 which is equivalent to:
y^2 - 4y - 6 = 0
use the quadratic equation to solve for the roots of this equation to get:
y = 2 +/- sqrt(10)
you get:
y = 2 + sqrt(10) or y = 2 - sqrt(10)
when you plug both of those solutions into the equation, the equation is true, so these solutions are good.
I cheated by using my calculator to confirm.
I'll confirm one by not cheating so you can see how I did it.
If we let y = 2 + sqrt(10), then the original equation of:
(1/y) + (1/(y+2) = 1/3 becomes:
(1/(2+sqrt(10)) + (1/(2+sqrt(10)+2) = 1/3
simplify to get:
(1/(2+sqrt(10)) + 1/(4+sqrt910)) = 1/3
multiply both sides of the equation by (2+sqrt(10))*(4+sqrt(10)) to get:
(4+sqrt(10) + (2+sqrt(10) = ((2+sqrt(10))*(4+sqrt(10))) / 3
Do the math and this comes out to be 6+2sqrt(10) = 6+2sqrt(10) which is true, confirming the solution is correct.
