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These are the correct factors for each part of the fractions. I know factoring
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can be tough, so if you're getting at least half of these right, great work. If
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you got stuck on one of these, try to look back at your work and see where you
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went wrong to get these factors. If you can't find an error in your work then
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stay with me for this solution. For our first numerator we can pull out a 2x
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from each term. So we'll have 2x times x squared minus 6x plus 9. Then we notice
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that this is a special factoring pattern. It's a perfect square trinomial. So we
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have 2x times x minus 3, times x minus 3. This gives us our first numerator. For
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this denominator, we want to find the factors of negative 12, that sum to
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negative 4. This allows us to rewrite our middle term. And then we'll use
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factoring by grouping to get 3x plus 2 times x minus 2. This is our factored
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form for our first denominator. For this numerator we want to find the factors
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of 12 that sum to negative 8. These two factors are negative 6, 6 and negative
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2. We'll use factoring by grouping to get 3x minus 2 time x minus 2 for this
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numerator. And finally for this last denominator we pull out a 6x from both
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terms leaving us with 6x times x squared minus 9. Then we can factor this
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difference of squares using x plus 3 times x minus 3. This difference of squares
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pattern appears in all sorts of math. So it's great that we can recognize it
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quickly.