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 2 solutions by mananth, MathTherapy:
Answer by mananth(16946) 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(10552) 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