I have not had algebra in a couple years and I can't remember the how to solve
this problem. I know the answer is supposed to be (-11/6), but I don't know how
they got that answer! 

2/(y+3)+ 3/(y-4)= 5/(y+6)

 2     3     5   
——— + ——— = ———
y+3   y-4   y+6

The LCD is (y+3)(y-4)(y+6)
           
Multiply every term by that over 1


 2  (y+3)(y-4)(y+6)    3  (y+3)(y-4)(y+6)    5  (y+3)(y-4)(y+6) 
———·——————————————— + ———·——————————————— = ———·———————————————
y+3        1          y-4        1          y+6       1

Now we cancel everything that will cancel:
      1                          1                          1 
 2  (y+3)(y-4)(y+6)    3  (y+3)(y-4)(y+6)    5  (y+3)(y-4)(y+6) 
———·——————————————— + ———·——————————————— = ———·———————————————
y+3        1          y-4        1          y+6       1
 1                     1                     1

      2(y-4)(y+6) + 3(y+3)(y+6) = 5(y+3)(y-4)

2(y2+6y-4y-24) + 3(y2+6y+3y+18) = 5(y2-4y+3y-12)

      2(y2+2y-24) + 3(y2+9y+18) = 5(y2-y-12)

2y2 + 4y - 48 + 3y2 + 27y + 54 = 5y2 - 5y - 60

                 5y2 + 31y + 6 = 5y2 - 5y - 60

Subtract 5y2 from both sides

                       31y + 6 = - 5y - 60

Subtract 6 from both sides

                           36y = -66
 
Divide both sides by 36

                             y = -66/36

Reduce fraction

                             y = -11/6

Edwin
AnlytcPhil@aol.com