SOLUTION: how do you solve this equation 2/(1-x) + 4/(2-x) = 11/6

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Question 24849: how do you solve this equation 2/(1-x) + 4/(2-x) = 11/6
Answer by AnlytcPhil(1806)   (Show Source): You can put this solution on YOUR website!
how do you solve this equation 2/(1-x) + 4/(2-x) = 11/6

 2     4     11
——— + ——— = ————
1-x   2-x     6

 2     4     11   
——— + ——— = ————
1-x   2-x     6

None of the denominators will factor.  They have no common factor, so
the LCD is their product 6(1-x)(2-x)
           
Multiply every term by that over 1
 
 2  6(1-x)(2-x)    4  6(1-x)(2-x)   11  6(1-x)(2-x) 
———·——————————— + ———·——————————— = ———·———————————
1-x      1        2-x      1         6      1       

Now we cancel everything that will cancel:

       1                      1         1
 2  6(1-x)(2-x)    4  6(1-x)(2-x)   11  6(1-x)(2-x) 
———·——————————— + ———·——————————— = ———·———————————
 1-x       1       2-x        1       6      1  
  1                 1                 1

                12(2-x) + 24(1-x) = 11(1-x)(2-x)

              24 - 12x + 24 - 24x = 11(2-x-2x+x2)
                
                         48 - 36x = 11(2-3x+x2) 
                   
                         48 - 36x = 22 - 33x + 11x2

                                0 = 11x2 + 3x - 26 
                                _____________
                          -3 ± Ö32-4(11)(-26) 
                     x = ——————————————————————    
                                   2(11)
                   
                                ____
                          -3 ± Ö1153 
                     x = ————————————    
                              22

solutions (approx.): x = 1.407084259  and x = -1.679811531 

Edwin
AnlytcPhil@aol.com
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