Question 120242
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solve for all values of x that satisfy the equation x/x+3=5/x+7
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The other person who responded saw the equation as: {{{x/x + 3 = 5/x + 7}}}, and ended up with the x-value, {{{- 5/3}}}. 
Most likely though, it's {{{x/(x + 3) = 5/(x + 7)}}}, with {{{matrix(1,3, x <> - 3, ", or", x <> - 7)}}}
                                    x(x + 7) = 5(x + 3) ---- Cross-multiplying
                                      {{{x^2 + 7x = 5x + 15}}}
                       {{{x^2 + 7x - 5x - 15 = 0}}}
                              {{{x^2 + 2x - 15 = 0}}}
                           (x - 3)(x + 5) = 0
                                          x - 3 = 0       OR        x + 5 = 0 ----- Setting each FACTOR equal to 0
                                                x = 3       OR               x = - 5

Both values for x make the equation true, they are neither - 3 nor - 7, and so, both are VALID/ACCEPTABLE!</font></font></font></b></pre>