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swissgirl 3 years ago Is anyone familiar with Continued-Fractions approximation?

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1. swissgirl

$${x^2+3x+2 \over x^2-x+1}$$

2. swissgirl

Like I sooo dont follow the process although everyone seems to say that it is simple

3. amistre64

continued fraction is simple, i spose this would follow its pattern

4. amistre64

...if i could recall how to do a continued fraction that is. i seem to have had misremembered the simple details :)

5. amistre64

$\frac{5}{12}=\frac{1}{\cfrac{12}{5}}=\cfrac{1}{2+\cfrac25}=\cfrac{1}{2+\cfrac1{\cfrac52}}=\cfrac{1}{2+\cfrac1{2+\frac12}}$stuff

6. estudier

This is something new, I think. A variant on polynomial division?

7. swissgirl

Right but how would u clean everything up in the end. Like the answer doesnt look like an escalator in my book

8. amistre64

hmm, how does it look in your book?

9. swissgirl

I do think its a variation of polynomial division The answer is $$1+{4 \over x- \frac{5}{4}} +{ \frac{21}{16} \over x + \frac{1} {4}}$$

10. estudier

I guess it's poly division as opposed to the usual integer division. It's not that clear how u get rid of the escalator, though....

11. estudier

Oh, I see...it stops pretty quickly and then you just add up the terms. So 1 + 1 over (blah above) and actually flipping it over so to speak...

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