SOLUTION: solve 9 + (2/(w-1)) = -4/(w-2) I got stuck at 9w^2 - 21w + 10 = 0 I can't foil it and when I clicked no solution it said it was incorrect

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: solve 9 + (2/(w-1)) = -4/(w-2) I got stuck at 9w^2 - 21w + 10 = 0 I can't foil it and when I clicked no solution it said it was incorrect      Log On


   

Question 773090: solve
9 + (2/(w-1)) = -4/(w-2)
I got stuck at 9w^2 - 21w + 10 = 0
I can't foil it and when I clicked no solution it said it was incorrect
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
9%22%22%2B%22%222%2F%28w-1%29 %22%22=%22%22 -4%2F%28w-2%29

Multiply every term by the LCD of red%28%22%22%2A%28w-1%29%28w-2%29%29

9red%28%22%22%2A%28w-1%29%28w-2%29%29%22%22%2B%22%222%2F%28w-1%29red%28%22%22%2A%28w-1%29%28w-2%29%29 %22%22=%22%22 -4%2F%28w-2%29red%28%22%22%2A%28w-1%29%28w-2%29%29

Cancel away the denominators:

9red%28%22%22%2A%28w-1%29%28w-2%29%29%22%22%2B%22%222%2F%28cross%28w-1%29%29red%28%22%22%2A%28cross%28w-1%29%29%28w-2%29%29 %22%22=%22%22 -4%2F%28cross%28w-2%29%29red%28%22%22%2A%28w-1%29%28cross%28w-2%29%29%29

   9(w-1)(w-2) + 2(w-2) = -4(w-1)
9(w² - 3w + 2) + 2w - 4 = -4w + 4

9w² - 27w + 18 + 2w - 4 = -4w + 4

         9w² - 25w + 14 = -4w + 4

         9w² - 21w + 10 = 0   <--- you got here and couldn't factor.

Use trial and error. The only ways to factor 9 is 9*1 and 3*3,
The only ways to factor 10 is 10*1 and 5*2

           (3w-5)(3w-2) = 0

       3w - 5 = 0;  3w - 2 = 0
           3w = 5;      3w = 2
            w = 5%2F3;       w = 2%2F3

Edwin