Question 37137
<pre><font size = 3><b>Solve for x:

   1         1          22
——————— + ——————— = —————————
 x - 4     x + 4     x² - 16

Factor the denominator on the right

   1         1             22
——————— + ——————— = ————————————————
 x - 4     x + 4     (x - 4)(x + 4)

Multiply each fraction through by the LCD = (x - 4)(x + 4)

Multiply first term on left by the LCD/1
                                           1
   1       (x - 4)(x + 4)       1       <s>(x - 4)</s>(x + 4)
——————— · ———————————————— = ——————— · ———————————————— =  (x + 4)  
 x - 4           1             <s>x - 4</s>           1 
                                 1
Multiply second term on left by the LCD/1
                                                  1
   1       (x - 4)(x + 4)       1       (x - 4)<s>(x + 4)</s>
——————— · ———————————————— = ——————— · ———————————————— =  (x - 4)  
 x + 4           1             <s>x + 4</s>           1 
                                 1

Multiply term on right by LCD/1

                                                                 1  
       22           (x - 4)(x + 4)           22           <s>(x - 4)(x + 4)</s>
———————————————— · ———————————————— = ———————————————— · ———————————————— = 22
 (x - 4)(x + 4)            1           <s>(x - 4)(x + 4)</s>            1 
                                              1

So the equation is now

             (x + 4) + (x - 4) = 22
                 x + 4 + x - 4 = 22
                            2x = 22
                             x = 11 

Edwin
AnlytcPhil@aol.com</pre>