SOLUTION: <pre>Solve for x: 1 1 22 ——————— + ——————— = ————————— x - 4 x + 4 x² - 16</pre>

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: <pre>Solve for x: 1 1 22 ——————— + ——————— = ————————— x - 4 x + 4 x² - 16</pre>      Log On


   

Question 37137This question is from textbook McDougal Littell
: 
Solve for x:

   1         1          22
——————— + ——————— = —————————
 x - 4     x + 4     x² - 16
 This question is from textbook McDougal Littell

Answer by AnlytcPhil(1806) About Me  (Show Source):
You can put this solution on YOUR website!
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       (x - 4)(x + 4)
——————— · ———————————————— = ——————— · ———————————————— =  (x + 4)  
 x - 4           1             x - 4           1 
                                 1
Multiply second term on left by the LCD/1
                                                  1
   1       (x - 4)(x + 4)       1       (x - 4)(x + 4)
——————— · ———————————————— = ——————— · ———————————————— =  (x - 4)  
 x + 4           1             x + 4           1 
                                 1

Multiply term on right by LCD/1

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