Question 24849
<pre>how do you solve this equation 2/(1-x) + 4/(2-x) = 11/6
<font size = 3><b>
 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:

       <sub>1</sub>                      <sub>1</sub>         <sub>1</sub>
 2  6<s>(1-x)</s>(2-x)    4  6(1-x)<s>(2-x)</s>   11  <s>6</s>(1-x)(2-x) 
———·——————————— + ———·——————————— = ———·———————————
 <s>1-x</s>       1       <s>2-x</s>        1       <s>6</s>      1  
  <sup>1</sup>                 <sup>1</sup>                 <sup>1</sup>

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

              24 - 12x + 24 - 24x = 11(2-x-2x+x<sup>2</sup>)
                
                         48 - 36x = 11(2-3x+x<sup>2</sup>) 
                   
                         48 - 36x = 22 - 33x + 11x<sup>2</sup>

                                0 = 11x<sup>2</sup> + 3x - 26 
                                _____________
                          -3 ± <font face = "symbol">Ö</font>3<sup>2</sup>-4(11)(-26) 
                     x = ——————————————————————    
                                   2(11)
                   
                                ____
                          -3 ± <font face = "symbol">Ö</font>1153 
                     x = ————————————    
                              22

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

Edwin
AnlytcPhil@aol.com</pre>