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Because subtraction of fractions can cause many errors, I like to change them into additions of the opposite:
There are several ways to simplify this expression. The way I like to do this is:
Find the Lowest Common Denomintor (LCD) of all the "little" denominators.
Multiply the numerator and denominator of the "big" fraction by the LCD found in step 1.
Let's see how this works on your problem.
1) Find the LCD of the "little" denominators. The "little" denominators are (a+b) and (a-b). The LCD of these two is simply their product: (a+b)(a-b)
2) Multiply the numerator and denominator of the "big" fraction by the LCD:
In both the numerator and denominator we will need to use the Distributive Property to multiply:
Now all the "little" denominators cancel out:
leaving:
which simplifies as follows:
The 2's cancel leaving
(