Given (14x + 22)/(x + 2) = -3x + 7, compute the sum of all the possible values of Express your answer as a fraction.
Rewrite (14x + 22) / (x + 2) = -3x + 7
as 24x + 22 = (-3x + 7)(x + 2)
1) Multiply out the right side.
2) Take all terms to the left side, forming a quadratic.
3) Use the quadratic formula to solve the equation.
4) Add together the two solutions, noting that the radicals cancel.