Respuesta :

altavistard
Using parentheses here would greatly reduce the ambiguity of your equation. At first I thought you'd written 1/3x    +     12, but then saw the possibility that you had meant 1 / (3x+12).  Big difference!

                                                                    2
Similarly -2/x2-16) could be written as - -----------  or as -2 / (x^2-16).  
                                                                  x^2-16

So: We need to solve  1 / (3x+12) - 2 / (x^2 -16) = 5 / (x+4).

At least, this is what I assume you have.

The LCD is 3(x-4)(x+4).  Mult. all three terms of the equation by this and reduce as appropriate:


3(x-4)(x+4)      3(x-4)(x+4)(2)       3(x-4)(x+4)(5)
---------------- - ---------------------  = ----------------------
   3(x+4)          (x-4)(x+4)               x-4

This reduces to x - 4 - 6 = 15(x+4)   =   15x + 60

Then x - 10 = 15x + 60, or -70 = 14x, or -5

Thus, x = -5/14.  You should definitely check this answer by subst. -5/14 for x in the original equation.  Is the equation then true?

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