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?
