There's very little difference between an addition problem and a subtraction problem when it comes to fractions; once you've found the LCD, you're going to subtract the numerators instead of adding them.

Example #1

Subtract -

Solution #1

In this very simple example, we have no factoring or reducing to do, and we can go straight to finding the LCD (six) and rewrite each fraction in terms of the LCD:

=  · =

=  · =

- = =

It's very important to remember that if the numerator is a polynomial, the negative gets distributed through the entire polynomial, effectively switching the signs of each term.

Example #2

Subtract -

Solution #2

Nothing can be factored/reduced, so we can begin by finding the LCD, which is (x - 1)(x + 1) since it must contain both (x - 1) and (x + 1).

Each fraction gets rewritten in terms of the LCD:

=  · =

=  · =

- = -

=  

=

=

This fraction is fully factored, and nothing cancels, so this is our final answer.

Obviously, the trickiest part of the subtraction problem is dealing properly with the negative sign, and distributing it where necessary. If you can get that, subtraction is just as easy as addition!

The Rules So Far

1. Any time you see a fraction, FACTOR the numerator and denominator.
2. Any time you have a fraction with factored numerator and denominator, REDUCE, by canceling common factors.
3. Multiplying fractions involves multiplying across the numerators, and multiplying across the denominators.
4. Dividing fraction is the same as multiplying the first fraction by the reciprocal of the second fraction.
5. To add fractions, perform the following steps:
   1. factor and reduce each fraction (steps 1 and 2)
   2. find the LCD
   3. convert each fraction to the LCD (and skip steps 1 and 2 on the new fractions!)
   4. add the numerators, using the distributive property if necessary, and combining any like terms you find
6. To subtract fractions, follow the same steps as adding fractions, except that you will subtract the second numerator from the first.

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