help in finding the error

Question

 

Describe and correct the error.

 

 

1.       3   +  6    =    8___

          x      x+3       x+1

 

         LCD = x(x+3) (x + 1)

         3(x + 3) (x + 1) + 6x(x + 1) = 8

         3(x^2 + 4x + 3) + 6x^2 + 6x = 8

         3x^2 + 12x+ 9 + 6x^2 + 6x = 8

          9x^2 + 18x + 1 = 0

                        ___________

       x = -18 ±√18^2 - 4(9)(1)

                       2(9)

             ___________                       __

       = √-18√±√288     =    -18 ± 12√2

                  18                        18

 

      x = -3± 2√2

                 3

 

Answer 1

L,

 

remember: what you do to one side of the equation you must do to the other.

 

3(x + 3) (x + 1) + 6x(x + 1) = 8x(x + 1)(x + 3)

 

3x² + 12x + 9 + 6x² + 6x = 8x³ + 32x² + 24x

 

8x³ + 32x² +24x = 3x² + 12x + 9 + 6x² + 6x = 9x² + 18x + 9

 

from which you should be able to figure out that

 

x = 3

 

 

 

Answer 2

 2nd line is not correct.

 

  It should be:

 

   3 ( X +3) ( X +1 ) + 6X ( X+1 ) = 8X  (X + 3)          Both sides of equation has been multiplied

                                                                               by LCD of the denominators.

 

   3 ( X^2 + 4X + 3 ) + 6X^2 + 6X = 8X^2 + 24X

 

 

   X^2 - 6 X + 9 = 0

 

    ( X -3 ) ^2 = 0

 

     X = 3

 

     Testing:

 

     3  +  6       =   8   

     3     3+3        3 +1

 

       1 + 1  = 2

 

          2 = 2