The numerator of a fraction is 1 less than the denominator. When both numerator and denominator are increased by 2, the fraction is increased by 1/12. Find the original fraction. (One should try to solve it by completing the square)

This is my attempt:

x+1/x+2-(x-1)/x=1/12

After that I multiplied everything with (x+2) 12x and cancelled out the numbers. I am not sure if the first equation is correct.