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Partial Fractions |
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| Jun26-09, 08:43 AM | #1 |
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Recognitions:
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Partial Fractions
I'm having trouble understanding what the numerator needs to be in the partial fractions.
e.g. [tex]\frac{1}{(x-1)(x-2)^2}\equiv \frac{A}{x-1}+\frac{Bx+C}{(x-2)^2}[/tex] Notice how the first numerator has a constant A, while the second is linear Bx+C. Actually... just now I think I may understand it. Does it have to do with the fact that during synthetic division, the remainder is always 1 degree less than the divisor? The second fraction's denominator is a quadratic, so its numerator should be linear? |
| Jun26-09, 09:25 AM | #2 |
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Recognitions:
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"Does it have to do with the fact that during synthetic division, the remainder is always 1 degree less than the divisor? The second fraction's denominator is a quadratic, so its numerator should be linear?"
Essentially - the numerator should always be the "most general" polynomial of lower degree than the denominator |
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