The roots of the equation x / (x + 2) + 3 / (x - 4) = (4x + 2) / (x 2 - 2x - 8) are Answers: A) x = 4 and x = 1 B) x = 4 only C) x = 1 only D) x = -4 only E) None
We first note that   (x + 2)(x - 4) = x 2 - 2x - 8   We now multiply all terms of the given equation by (x + 2)(x - 4) and simplify to get   x (x - 4) + 3 (x + 2)= (4x + 2)   Expand, group and solve   x 2 - x + 6 = 4x + 2   x 2 - 5x + 4 = 0   (x - 1)(x - 4) = 0   Roots: x = 1 and x = 4   Check answer: only x = 1 is a solution since the given equation is not defined at x = 4.   Answer x = 1 only
<result>C</result>
The roots of the equation x / (x + 2) + 3 / (x - 4) = (4x + 2) / (x 2 - 2x - 8) are