Respuesta :

altavistard
It would be best if you were to enclose each denominator inside parentheses.  Otherwise I have to take an educated guess regarding what you meant:

                                      1        1               x - 2
1/x+1/x-3=x-2/x-3  =>  ----- + ------ =     ----------
                                       x       x-3            x - 3

The LCD here is x(x-3).

x-3            x          x(x-2)
------- + --------- = -------------
LCD        LCD       LCD

Then x-3+x=x^2 -3x,         or           2x-3=x^2-3x        or     x^2 - 5x - 3 = 0


Using the quadratic formula to solve for x:

        5 plus or minus sqrt(25-4(1)(-3)
x = --------------------------------------------
                             2

          5 plus or minus sqrt( 25 + 12)
   = --------------------------------------------
                             2

There are 2 solutions.  Complete the arithmetic to find them.
  Be sure to check both answers via subst. into the original equation.

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