Question

1/(y-1)(y-2) = A/(y-1)+B/(y-2)
How to do you find A and B?

Answer 1

there is two why simple one and exact one

Answer 2

i need the exact one, i suppose

Answer 3

let me explain them for you :
the exact one tells multiplay second side and compare nominator of both side.

Answer 4

i mean : a(y-2)+b(y-1)= (a+b)y-(2a+b)

Answer 5

know you can cancel both side dominator with each other .

Answer 6

now compare what remains, coefficient of y with same degree should be equal .

Answer 7

look at your first equation you just have 1 . it 's equal with 0*y + 1

Answer 8

so 0 = a+b
-2a-b=1
a=-1 b=1

Answer 9

if you get this way i could tell you the simple way

Answer 10

ok i'm trying to understand...

Answer 11

if u have any problem you could ask

Answer 12

a(y-2)+b(y-1)= (a+b)y-(2a+b) how do you get the right part (after the = sign)?

Answer 13

oh no it's ok, i got it...

Answer 14

sorry i was busy with another question

Answer 15

what do you mean by the coefficient of y should be equal?

Answer 16

the idea is compare
(for example)

2y^2 + 3y + 1 = ay^2 + by + c

in this example, for the two sides to be equal (for all y), it requires that a is 2, b is 3 and c is 1

use that same idea in your problem.

Answer 17

in your problem you have

1 = (a+b)y-(2a+b)

Answer 18

i don't know the exact word in english but phi get what i mean

Answer 19

or
0y + 1 = (a+b)y-(2a+b)

Answer 20

why do you put 0y? for what purpose?

Answer 21

we started with
1/(y-1)(y-2) = A/(y-1)+B/(y-2)

and (after getting a common denominator)
\[ \frac{1}{(y-1)(y-2)} = \frac{(A+B) y - (2A+B)}{(y-1)(y-2)}\]

equate the numerators
\[ 1=(A+B) y - (2A+B) \]
or because you have a y term on the right side, explicitly show a y term on the left side
\[ 0y+ 1=(A+B) y - (2A+B) \]

Answer 22

now you can "match coefficients"

Answer 23

@ phi : thanks you tough me a new word

Answer 24

so A+B = 0 and -(2A+B) = 1

Answer 25

yes, now you have to solve 2 simultaneous equations

Answer 26

and now its easy thanx a lot

Answer 27

A=1 and B=-1

Answer 28

A=-1 and B =1

Answer 29

oh yes right

Answer 30

actually no i get B=-1

Answer 31

that's ur answer so A+B = 0 and -(2A+B) = 1
a=-b
2a+b=-1
2a-a=-1
a=-1
a=-b b=1

Answer 32

oh yeah sry