Question 268557
<pre>
please help me solve this equation: x/x+1-2=3/x-3
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{{{x/(x + 1) - 2 = 3/(x - 3)}}}, with {{{system(x <> - 1,  x <> 3)}}}
x(x - 3) - 2(x + 1)(x - 3) = 3(x + 1) ---- Multiplying by LCD, (x + 1)(x - 3)
  {{{x^2  -  3x  -  2(x^2  -  2x  -  3) = 3x + 3}}}
       {{{x^2  -  3x  -  2x^2 + 4x + 6 = 3x + 3}}}
       {{{x^2 - 2x^2 - 3x + 4x + 6 = 3x + 3}}}
                       {{{- x^2 + x + 6 = 3x + 3}}}
       {{{0 = x^2 + 3x - x + 3 - 6 = 0}}}
                       {{{x^2 + 2x - 3 = 0}}}
                 (x - 1)(x + 3) = 0 --- Factorizing the trinomial
 x - 1 = 0      OR    x + 3 = 0 --- Equating each binomial to 0
       x = 1      OR           x =  -  3 
 
Neither of the 2 solutions is - 1 or 3, so BOTH are VALID!</font></font></font></b></pre>