When you have to add or subtract rational expressions with different denominators, how can you find a common denominator to use?

First you reduce each fraction to lowest terms by dividing both the numerator and denominator by their greatest common divisor. After this you reduce the fractions to their lowest common denominator which is the least common multiple of the denominators of all fractions. You can find the least common multiple between numbers by decomposing them in their prime factors. In some cases, you might also associate two particular terms first for simplification, here an example: 3/7 + 2/3 + 4/7 = (3/7 + 4/7) + 2/3 = 7/7 +2/3 = 1/1 + 2/3 = 3/3 + 2/3 = 5/3 Further information: http://en.wikipedia.org/wiki/Lowest_common_denominator http://en.wikipedia.org/wiki/Least_common_multiple http://en.wikipedia.org/wiki/Greatest_common_divisor

The fastest way to do it is to simply multiply the two denominators, but that will not often turn out to be your LCD. If you are looking for the LCD, then just work your way up by multiplying by 2,3,4, etc. until you have a match. (i.e. 6 and 8. 6x8=48 but the LCD is 6x4=24=8x3)