Question

Calculus 2,

Can you tell me just how do I find "A" in this improper fraction ?
https://dl.dropboxusercontent.com/spa/y0bfo3ob2bxd2dn/tlb-q5ix.jpg

Answer 1

i do not see an "A"

Answer 2

I mean if I split it it will be A/something + B/somethingelse + C/anothersomethingelse

Answer 3

I have to solve it by splitting it

Answer 4

ah, decomps

Answer 5

yea

Answer 6

\[\frac{A}{x}+\frac{B}{x^2}+\frac{C}{x-1}\] is a start

Answer 7

but how do I find that A here

Answer 8

i might start with -x+x up top

3x^2 -x +1 -x +x

3x^2 -2x + 1+x
-------- -------
x^3-x^2 x^3-x^2

that should help reduce the work

Answer 9

B and C are cover up method

Answer 10

A is messy for a weird reason

Answer 11

if you know B and C, the rest is substituting in for some random x

Answer 12

i like the "cover up" method, but it will not work for \(A\)

Answer 13

I have to substitute here ?? https://www.dropbox.com/s/den0s8zlbii894h/Screenshot%202013-10-29%2015.11.28.jpg

Answer 14

@amistre64 good morning!

Answer 15

hi satellite :)

Answer 16

where r u from and its a morning ?

Answer 17

im in florida ..

Answer 18

aha

Answer 19

\[Ax(x-1)+B(x-1)+Cx^2=3x^2-x+1\]

Answer 20

bahamas

Answer 21

did you find \(C\) ?

Answer 22

I know C and B

Answer 23

i wish i was in the bahamas
what is C?

Answer 24

B = -1 C= 3

Answer 25

1+x = A(x)(x-1) + B(x-1) + C(x^2)

id say lets x = -1, and sub in your B and C values

Answer 26

then \(3x^2+Ax^2=3x^2\implies A=0\)

Answer 27

on the left the two terms with \(x^2\) are \(Ax^2+Cx^2\) on the right it is \(3x^2\)
if you know \(C=3\) then it follows that \(A=0\)

Answer 28

what if I solve for x=2

Answer 29

now to me it shows A= 26/4

Answer 30

oh wait

Answer 31

I think I messed up in one thing, please tell me

Answer 32

class is starting .... yall kids play nice ;)

Answer 33

if I chose x=2 how is that expression gonna change ? 1+x = A(x)(x-1) + B(x-1) + C(x^2)

Answer 34

\[Ax(x-1)+B(x-1)+Cx^2=3x^2-x+1\]\(A=3,B=-1\)
\[Ax(x-1)-(x-1)+3x^2=3x^2-x+1\]
enjoy your class

Answer 35

bb amistre

Answer 36

that tells you right away that \(A=0\)

Answer 37

if you choose \(x=2\) you still get \(A=0\)

Answer 38

ohh I see, thanks a lot

Answer 39

yw