Calculus (Partial Fractions)
posted by Sean .
My Calculus class just started Partial Fractions, and I understand MOST of it.
I'm having a slight problem though, when either C, or C and D come in.
I understand
A/(something) + B/(something)
But I become confused when it's either
A/(something) + B/(something) + C/(something)
OR
A/(something) + B/(something) + (Cx + D)/(something)
Why is it that you get ONLY C, or Cx + D ?
I always get confused when it comes to that, so help would be greatly appreciated.

When you have a quadratic that does not have real roots in the denominator (complex roots only), you put Cx+D in the numerator.
like if your denominator were (x1)(x+1)(x2)
you might use
A/(x1) + B/(x+1) +C/(x2)
But if your denominator were:
(x1)(x^22x+2)
You could deal with the (x1) part just fine.
but what to do with the other part?
You can not write it as the sum of two fractions with numerators B and C because you can nor write
x^22x+2 as (x+p)(x+q)
so you have to resort to
(C + D x)/(x^22x+2) 
This method has practical applications only if the denominator factors.
Since you don't give an example I will supply one
separate (5x^2+3x+4)/(x^3+x^22x)
(I started with known fractions and simplified, so that I would have a question that worked out)
The bottom factors to x(x+2)(x1)
so let
(5x^2+3x+4)/(x^3+x^22x) = A/(x+2) + B/(x1) + c/x
(5x^2+3x+4)/(x^3+x^22x)
= [Ax(x1) + Bx(x+2) + C(x+2)(x1)]/x(x+2)(x1)
clearing the denominator we get:
5x^2+3x+4 = Ax(x1) + Bx(x+2) + C(x+2)(x1)
now let x=0, then 2C = 4, and C = 2
let x=1, then 3B=12, and B = 4
let x=2, then 6A = 18 and A = 3
so my original fraction (5x^2+3x+4)/(x^3+x^22x) can
be split into
3/(x+2) + 4/(x1)  2/x 
Reiny. You misunderstood. And I didn't word it right.
I meant where does (Cx + D)/Something
Pop up? 
Okay. Example.
If the Denominator is
x^4  2x^2  8 > (x2) (x+2) (x^2+2)
Would I do A + B + C, or A + B + (Cx + D)? 
Wow. I'm making this topic last a while.
I think and this is just out loud that you would do (Cx + D) Over the X^2 + 2?
Am I getting that right?
OR
You have Cx + D over something if the SOMETHING has a term of X to a power greater than one?
Respond to this Question
Similar Questions

Calc easy
Having trouble getting the correct solution. The integral of “x squared” in the numerator and “x squared plus x minus 6” in the denominator. S X2 / (X2 + x – 6) dx Thanks! That's a messy one. According to my table of integrals. … 
Partial Decompostion Fractions
Can you please help me with the following questions please, I don't understand them. I know the general rule about them. Write the partial fraction decomposition of the rational expression. (x^2+4x1)/(x^2+3)^2 (4x^3+4x^2)/(x^2+5)^2 
AlgebraPartial Fractions
Can you please help me with the following questions please, I don't understand them. I know the general rule about them. Write the partial fraction decomposition of the rational expression. (x^2+4x1)/(x^2+3)^2 (4x^3+4x^2)/(x^2+5)^2 
Partial Fractions
I think and this is just out loud that you would do (Cx + D) Over the X^2 + 2? 
Calculus  Partial Fractions
What is the integral of 7e^(7t) Divided By e^14t+13e^7t+36 Using partial fractions 
Calculus  Partial Fractions
I've set a problem up, something like this. s^4: A+D=0 s^3: 2A+B3D+E=0 s^2: 2AB+C+3D3E=0 s^1: 2A+BD+3E=4 s^0: A+CE=4 
Calculus  Integrals
I made this question, just wanted to make sure it didn't drown under the tide... I've set a problem up, something like this. s^4: A+D=0 s^3: 2A+B3D+E=0 s^2: 2AB+C+3D3E=0 s^1: 2A+BD+3E=4 s^0: A+CE=4 Count Iblis It's easier to … 
Calculus  Integration
I came across this problem in my homework, and I was wondering if partial fractions would be rational for this problem. Int [(2x)/((x^2)^2)]dx If I don't use partial fractions, what would I use? 
calculus
I am working on this problem and having some trouble. We're supposed to use partial fractions. The problem is: integral of dx / (x^61) . I got the values of A and D, but I am having trouble with the others. Help please! 
Math Partial Fractions
Decompose the following into partial fractions after factoring the denominator as much as possible. Please show some work so I can understand how you did it. 1)x^2/((x1)(x^2+5x+4)) 2)(3x^35x^2+12x+4)/(x^416) 3)1/(x^2 (x+1)^2 ) 4)(x+1)/((x^2+1) …