Expert: Lynn Houston - 4/28/2010

Question
find all real solutions of the equation:
x+2/x-2 = 3x/3x-6

Answer
x+2/x-2 = 3x/3x-6  get rid of the fractions by multiplying both sides by (x-2)(3x-6)

x+2(x-2)(3x-6)/x-2 = 3x(x-2)(3x-6)/3x-6  x-2 cancel on left and 3x-6 cancel on right side

x+2(3x-6) = 3x(x-2)  do the multiplication
3x^2 -12 = 3x^2 - 6x  subtract 3x^2, add 6x  and add 12 to both sides

6x = 12 divide both sides by 6

x = 2  HOWEVER, the solution cannot be 2 because that would give you a zero divisor, so there is no solution set for this problem.