SOLUTION: Please help me solve this equation: y+1/y+6-y/y^2-36=y-3/y-6

Question 132881: Please help me solve this equation:
y+1/y+6-y/y^2-36=y-3/y-6
Answer by nycsharkman(136) (Show Source): You can put this solution on YOUR website!
What you have is called a fractional equation.
You need to find the LCD and then multiply every fraction on both sides of the fractional equation by the LCD.
Your LCD is y^2 - 36 = (y - 6) (y + 6). It just so happens that this LCD is also a difference of two perfect squares, which works out wonderfully for us.
(y + 1)/(y + 6) times (y - 6) (y + 6) = (y + 1)(y - 6).
-y times (y - 6) (y + 6) = -y.
(y - 3)/(y - 6) times (y - 6) (y + 6) = (y - 3)(y + 6)
We now have this:
(y + 1) (y + 6) - y = (y - 3)(y + 6)
y^2 + 7y + 6 - y = y^2 + 3y - 18
Combine like terms AFTER you cancel the y^2 terms.
We are left with:
7y + 6 - y = 3y - 18
6y + 6 = 3y - 18
Solve for y.
6y - 3y = -6 - 18
3y = -24
y = -24/3
y = -8
To find out if I am right, replace all the y letters in the ORIGINAL equation that was given to you and simplify. If you get the same answer on both sides of the equation, then you will know that I'm right about y = -8.
Did you follow?

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