Question

write the partial fraction decomposition of
(X^3 + 4x - 1)/(X^3 - X^2)

Answer 1

hmmm the degrees are the same so your have to divide first

Answer 2

yeah i think polynomial division is what you need here

Answer 3

yikes and it is a drag after that to because of repeated root.

Answer 4

can't you then use partial fractions with remainder

Answer 5

cow is right

Answer 6

you need long division here first

Answer 7

yes sure. but you will still have a repeated root because denominator is
\[x^2(x-1)\] so you are going to have to write
\[\frac{A}{x}+\frac{B}{x^2}+\frac{C}{x-1}\] have fun. i would use technology.

Answer 8

ok i did the division and get 1 + (X^2 + 4X -2)/(X^3 - X^2)

Answer 9

ok so now you set up
\[\frac{A}{x}+\frac{B}{x^2}+\frac{C}{x-1}=\frac{x^2 + 4x -2}{x^3 - x^2}\] assuming your division is right

Answer 10

1
-----------------------
x^3-x^2 | x^3 +0x^2 +4x -1
-(x^3 -x^2)
----------------------------
1x^2+4x-1
so we have
\[\frac{x^3+4x-1}{x^3-x^2}=1+\frac{x^2+4x-1}{x^3-x^2}\]
now we can do partial fractions

Answer 11

@myininaya he got something else. you sure you are right?

Answer 12

you can't do
\[\frac{A}{x-1} + \frac{Bx+C}{x^{2}}\]
?

Answer 13

nope

Answer 14

am i wrong?

Answer 15

you have to take all powers.

Answer 16

oh i don't know because i didn't do it. he wrote something else. give me a second

Answer 17

i think i did my division right

Answer 18

hes write i mistype

Answer 19

sorry

Answer 20

i'm a her

Answer 21

lol i think im gonna change my icon to something more girly

Answer 22

why should i doubt you (honorary male tonight i see)

Answer 23

nothing too lewd i trust

Answer 24

\[\frac{A}{x}+\frac{B}{x^2}+\frac{C}{x-1}=\frac{x^2 + 4x -1}{x^3 - x^2}\]

Answer 25

i mistype that too i meant she not hes

Answer 26

:)

Answer 27

\[Ax(x-1)+B(x-1)+Cx^2=x^2+4x-1\] right so far?

Answer 28

i let x = 0 get B = 1 right off the bat

Answer 29

satellite
i think either way might work

\[= 1 + \frac{-3x+1}{x^{2}} + \frac{4}{x-1}\]
it matches same graph, so it works

Answer 30

sure but you still have that middle term right? so you can do pfd on it as well

Answer 31

oh yeah
-3/x and 1/x^2

Answer 32

i guess what i am saying is "you are not done yet"

Answer 33

ok so i guess we are done right? it is
\[1-\frac{3}{x}+\frac{1}{x^2}+\frac{4}{x-1}\]

Answer 34

yep

Answer 35

i only got as far as B = 1, but i guess armed with that the other two are easy. for example let x = 1, then c = 4 and we know that A+C=1 so A = -3 and we have them all

Answer 36

wow! thanks i need more practice