using partial fraction decomposition, decompose the fraction ((x^2)+x)/((x+2)((x-1)^2))

Question

anonymous · Answer

$$\frac{ x ^{2}+x }{ (x+2)(x-1)^{2} }$$

anonymous · Answer

yup :)

zepdrix · Answer

$$\Large \frac{x^2+x}{(x+2)(x-1)^2}=\frac{A}{x+2}+\frac{B}{(x-1)}+\frac{C}{(x-1)^2}$$

All of the factors in our denominator are `linear` so the numerators should all be `constant`. (One degree lower than the denominator factor).

We have a repeated linear factor, (x-1)(x-1), so we have to do this fancy thing with the repeating.

anonymous · Answer

ok good i did that part correctly... i was just getting weird fractions for a, b, and c and wanted to make sure i was setting it up correctly.... did you get 2/9 for a, 7/9 for b, and 2/3 for c?

zepdrix · Answer

mm lemme burn through it real quick and find out.

anonymous · Answer

ok thanks!!1

zepdrix · Answer

A and C, yes I agree.
But I got B=1.
Lemme try that again real quick. I prolly made a mistake in there.

zepdrix · Answer

Yah 7/9, that sounds right :) looks good!

anonymous · Answer

ok thank you so much!! and then when i put this back into the fraction would it be like $$\frac{ 2 }{9(x+2) }+\frac{ 7 }{9(x-1) }+\frac{ 2 }{9(x-1)^2 }$$

anonymous · Answer

wait the last one should be a three in the denominator

zepdrix · Answer

yah a 3.

Yes that's a nice way to write it, moving the denominator of the top fraction into the bottom like that. Make's it easier to read :)

anonymous · Answer

ok thank you so much for your help!!!