Question

Express Partial fraction
2x^2+3x+2/x^2+3x+2
@Luigi0210

Answer 1

Alright, do you remember what we did on the last one?

Answer 2

yes

Answer 3

Notice how they have the same powers, start by simplifying that first

Answer 4

How to get 2 from this questions

Answer 5

2 as the leading constant?

Answer 6

Nvm, I'll simplify it first

Answer 7

x^2+3x+2= (x+1)(x+2)
It can also be =(x+2)(x+1)
Will this difference affect the final answer

Answer 8

no..there no restriction for arrangement of terms..you can alternate them...

Answer 9

\[\Large \frac{2x^2+3x+2}{x^2+3x+2}=\frac{2x^2}{x^+3x+2}+\frac{3x+2}{x^2+3x+2}\]

\[\Large =2+(\frac{3x+2}{(x+2)(x+1)})\]

Answer 10

That should be x^2+3x+2, not x+3x+2, Whoops

Answer 11

thats not correct,
please do long division

Answer 12

the method itself is not correct

Answer 13

So, long division is the only method to get 2

Answer 14

@hartnn

Answer 15

long divsion or adjusting the numerator (which does not work always)
here, long division is the only option

Answer 16

okay

Answer 17

if co-efficients of highest power of x in num. and denom. are equal, only then , adjusting the numerator will work .

Answer 18

example :
Num = x^2 +ax+b
Denom = x^2 +cx+d

Then we express Num. as [x^2 + cx+d] - (ax+b)
and then separate the numerator

Answer 19

ok

Answer 20

x^2/(x+1)(x+2)= A/(x+1)+ B(x+2)

x^2/(x+2)(x+1)=A(x+2) + B(x+1)
Are these considered the same
Will it affect the final answer?

Answer 21

why just x^2 ?

Answer 22

Sorry, I don't get you

Answer 23

lets try adjusting the numerator here

\(2x^2+3x+2 = 2 (x^2+3x+2) - (3x-2)\)

now you can separate out the numerator

Answer 24

\(2x^2+3x+2 = 2 (x^2+3x+2) - (3x+2)**\)

Answer 25

2- (3x+2)/(x^2+3x+2)

now you can apply partial fractions method on (3x+2)/(x^2+3x+2)

Answer 26

@hartnn

Answer 27

that is denominator
i expressed numerator in terms of denominator

Answer 28

Okay

Answer 29

let me give you a general example :

if numerator = Ax^2 +Bx+C
and denominator = Dx^2 +Ex+F

then i express num = Ax^2 +Bx+C as

A/D(Dx^2 +Ex+F) - (AE/Dx +AF/D) + Bx+C

it may seem not so easy, but with specific examples and some practice, you will get hold of it

Answer 30

let me take some numbers

N = 3x^2 +4x+5
D = x^2 +9x+10

so i will express N as
3 (x^2 +9x+10) - (23x+ 25)