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To subtract fractions the denominators must be the same. So we start by finding a common denominator. The Lowest Common Denominator (LCD) for these two denominators is simply the product of the two denominators. We will multiply the numerator and denominator of each fraction by the other fraction's denominator:
In the numerators we just just the distributive property. In the denominators we can use FOIL. But we can also use the pattern to make it very easy:
which simplifies as follows:
Now we can subtract. One must be careful to subtract both parts of the second numerator. The 's cancel each other out. But the 's do not cancel!:
This is the simplified answer.
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