swissgirl Group Title Is anyone familiar with Continued-Fractions approximation? one year ago one year ago

1. swissgirl Group Title

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

2. swissgirl Group Title

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

3. amistre64 Group Title

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

4. amistre64 Group Title

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

5. amistre64 Group Title

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

6. estudier Group Title

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

7. swissgirl Group Title

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

8. amistre64 Group Title

hmm, how does it look in your book?

9. swissgirl Group Title

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 Group Title

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 Group Title

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...