Question

Solve: x + x/(x -2) = 2/(x - 2)

Answer 1

x + x/(x -2) = 2/(x - 2)


x(x -2) + (x -2)(x/(x -2)) = (x -2)(2/(x - 2)) ... Note: Multiply EVERY term by the LCD x-2 to clear out the fractions


x(x -2) + x = 2


x^2 - 2x + x = 2


x^2 - 2x + x - 2 = 0


x^2 - x - 2 = 0


(x-2)(x+1) = 0


x-2 = 0 or x+1 = 0


x = 2 or x = -1


Now if x = 2, then the denominators in the original equation will be equal to zero. Remember that dividing by zero isn't defined. So x = 2 is not allowed.


So the only solution is x = -1