To subtract ANY two fractions, you don't need a common denominator. Yes, it helps, but it's not needed. What I would do is this;
Multiply the numerator of the first one and the denominator of the second one. Now multiply the denominator of the first one and the numerator of the second one. Subtract these two values, and this will be the numerator of the answer. For the denominator of the answer, simply multiply the two denominators together. So, in essence;
$\displaystyle a/b - c/d = (ad - bc)/(bd)$
It looks complicated, but take this example;
$\displaystyle 5/6 - 7/9 = (45 - 42)/54$