Question 773090
<pre>
{{{9}}}{{{""+""}}}{{{2/(w-1)}}} {{{""=""}}} {{{-4/(w-2)}}}

Multiply every term by the LCD of {{{red(""*(w-1)(w-2))}}}

{{{9}}}{{{red(""*(w-1)(w-2))}}}{{{""+""}}}{{{2/(w-1)}}}{{{red(""*(w-1)(w-2))}}} {{{""=""}}} {{{-4/(w-2)}}}{{{red(""*(w-1)(w-2))}}}

Cancel away the denominators:

{{{9}}}{{{red(""*(w-1)(w-2))}}}{{{""+""}}}{{{2/(cross(w-1))}}}{{{red(""*(cross(w-1))(w-2))}}} {{{""=""}}} {{{-4/(cross(w-2))}}}{{{red(""*(w-1)(cross(w-2)))}}}

   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 = {{{5/3}}};       w = {{{2/3}}}

Edwin</pre>