SOLUTION: 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!

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Question 24549: 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)
Found 2 solutions by longjonsilver, AnlytcPhil:
Answer by longjonsilver(2297) About Me  (Show Source):
You can put this solution on YOUR website!
2%2F%28y%2B3%29%2B+3%2F%28y-4%29=+5%2F%28y%2B6%29

OK...need to get rid of the denominators..the fractions. To do this, we multiply every term by (y+3)(y-4)(y+6) and cancel out the ones we can, to leave:


2%28y-4%29%28y%2B6%29%2B+3%28y%2B3%29%28y%2B6%29+=+5%28y%2B3%29%28y-4%29
2%28y%5E2%2B2y-24%29%2B+3%28y%5E2%2B9y%2B18%29+=+5%28y%5E2-y-12%29
2y%5E2%2B4y-48%2B+3y%5E2%2B27y%2B54+=+5y%5E2-5y-60
5y%5E2%2B31y%2B6+=+5y%5E2-5y-60
31y+6 = -5y-60
36y + 6 = -60
36y = -66
y = -66/36
y = -11/6

there you go!

jon.

Answer by AnlytcPhil(1806) About Me  (Show Source):
You can put this solution on YOUR website!
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