Question

Partial Fractions Decomposition

Answer 1

\[\frac{ x+4 }{ x ^{2} (x ^{2}+4)}\]


How would you solve this faster

Answer 2

You will get\[\frac{ A }{ x }+\frac{ b }{ x ^{2} }+\frac{ Cx+D }{ x ^{2}+4 }\]

Answer 3

I tried the plugging numbers for x and i didn't work because of C cant't be factored so i would have to use the system of equations way, which i hate..

Answer 4

LCD all of them. then you'll have 4 equations to solve for A B C and D x.x !

Answer 5

Yea i got that part, its the system of equations i have now

Answer 6

this is partial fractions by the way

Answer 7

\[x+4=A(x)+B(x ^{2}+4)+Cx+D(x ^{2})\]

Answer 8

OH i put nonlinear didnt i LOL

Answer 9

I'm doing this in a paint file and will upload it

Answer 10

Ok thanks

Answer 11

agent get off... I got this

Answer 12

The more help the better :D

Answer 13

nah *shoots agent*

Answer 14

Well one you put the answer in log form for some reason which is wrong but you got A like i did but the rest is hard to follow D;

But he/she can help :D one can't do it alone

Answer 15

wait actually i think you got it right, but its just hard to follow what you did

Answer 16

of course I got it right and solved for A B C D which you need to do first.

Answer 17

and then you need to take antiderivative of each section

Answer 18

Options are to plug in values for x (this can often shorten the process)
Then after that, compare coefficients of like terms, with systems of equations

But you didn't seem to multiply by the LCD correctly, @jagr2713

@UsukiDoll he never mentioned this was an integration problem...

Answer 19

-_- ugh why even bother going back to this site. *rolls eyes*

Answer 20

antiderivative? Woah, lets calm it down guys.. :D Lets not spam

Answer 21

the first part when you split up the equation was right. Anything to do with factoring is its own fraction, but since you can't take the factor of x^2+4 you need Cx+D on that

Answer 22

Oh i didn't? @agent0smith

Question in @UsukiDoll link the ones in read, the 0 and 1, is that the number of x^3 and x's on the left side?

Answer 23

then the lcd is x^2(x^2+4) so that's a number to do and then distribute afterwards you'll have these equations that you'll need to solve for A B C and D

Answer 24

did you see how I left the x^3, x^2 x behind.. I was trying to match the original equation
the numerator had only x +4 so for the x part set that equal to 1 and for the constant part set that equation equal to 4

Answer 25

you don't have anything like this

if you did all your equations would be set to 1 for the x's and 4 for the constant

Answer 26

Would you mind rewriting after the red please so i can see better what you did up to the D and B

Answer 27

#no

Answer 28

though it's best to leave out the x parts