Writing and solving an equation of ratios is the way to go here. See if you can figure out why the following is correct:
x+3 x
----- = -------
12 x+3
Then (x+3)^2 = 12x, and x^2 + 6x + 9 = 12x, so that x^2 - 6x + 9 = 0
This is the square of (x - 3). Thus, x-3 = 0, and x = 3.
The value of x is 3.
