SOLUTION: Solve by the LCM method: {{{6/(y+3)+ 2/y =(5y-3)/(y^2-9)}}} I am unable to come up with the LCD: (y+3)(y-3)? Unsure of how to work this. Once I have the LCD, I believe I wi

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Solve by the LCM method: {{{6/(y+3)+ 2/y =(5y-3)/(y^2-9)}}} I am unable to come up with the LCD: (y+3)(y-3)? Unsure of how to work this. Once I have the LCD, I believe I wi      Log On


   

Question 299158: Solve by the LCM method:
6%2F%28y%2B3%29%2B+2%2Fy+=%285y-3%29%2F%28y%5E2-9%29
I am unable to come up with the LCD: (y+3)(y-3)? Unsure of how to work this. Once I have the LCD, I believe I will be able to solve it. Thank you in advance for your help.
Found 3 solutions by mananth, MathTherapy, ikleyn:
Answer by mananth(16949) About Me  (Show Source):
You can put this solution on YOUR website!
6%2F%28y%2B3%29%2B+2%2Fy+=%285y-3%29%2F%28y%5E2-9%29
6 / y+3 -5y-3 / y^2-9= 2/y
6(y-3) - (5y-3) / y^2-9 = 2/y
6y-18 -5y+15 = 2(y^2-9) /y
y-3= 2(y^2-9) /y
y(y-3)= 2 (y^2-9)
y= 2(y+3)(y-3) / (y-3)
y=2(y+3)
y=2y+6
y=-6
Ananth

Answer by MathTherapy(10839) About Me  (Show Source):
You can put this solution on YOUR website!
Solve by the LCM method:
6%2F%28y%2B3%29%2B+2%2Fy+=%285y-3%29%2F%28y%5E2-9%29

6%28y%29%28y+-+3%29+%2B+2%28y%5E2+-+9%29+=+y%285y+-+3%29-------- Multiply by LCD, y%2A%28y+-+3%29%28y+%2B+3%29%29

6%28y%5E2+-+3y%29+%2B+2y%5E2+-+18+=+5y%5E2+-+3y

6y%5E2+-+18y+%2B+2y%5E2+-+18+=+5y%5E2+-+3y

6y%5E2+%2B+2y%5E2+-+5y%5E2+-+18y+%2B+3y+-+18+=+0

3y%5E2+-+15y+-+18+=+0

3%28y%5E2+-+5y+-+6%29+=+3%280%29

y%5E2+-+5y+-+6+=+0

(y - 6)(y + 1) = 0

highlight_green%28y+=+6%29 or highlight_green%28y+=+-+1%29

Answer by ikleyn(53875) About Me  (Show Source):
You can put this solution on YOUR website!
.
Solve by the LCM method:
6%2F%28y%2B3%29 + 2%2Fy = %285y-3%29%2F%28y%5E2-9%29.
I am unable to come up with the LCD: (y+3)(y-3)? Unsure of how to work this.
Once I have the LCD, I believe I will be able to solve it. Thank you in advance for your help.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~


        The solution in the post by @mananth is incorrect.
        I came to bring a correct solution. 


LCM (the Least Common Multiple) is y*(y^2-9) = y*((-3)*(y+3).

So, we multiply both sides of the given equation by this expression y*(y-3)*(y+3).
We get

    6y*(y-3) + 2(Y^2-9) = (5y-3)y,

    6y^2 - 18y + 2y^2 - 18 = 5y^2 -3y,

    3y^2 - 15y - 18 = 0,

    y^2 - 5y - 6 = 0,

    (y-6)*(y+1) = 0.


The roots are  y = 6  and/or  y = -1.


ANSWER.  The solutions for the given equation are  y= 6  and/or  y = -1.


To  highlight%28highlight%28check%29%29,  I used a free of charge plotting tool at web-site  http:\\www.desmos.com/calculator/


I printed the formulas for the left side and right side functions and got two plots.

They have exactly two intersection points at y = 6  and  y = -1  , confirming my solution.

Solved correctly.