# Calculus (Partial Fractions)

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.

1. 👍
2. 👎
3. 👁
1. 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 (x-1)(x+1)(x-2)
you might use
A/(x-1) + B/(x+1) +C/(x-2)
But if your denominator were:
(x-1)(x^2-2x+2)
You could deal with the (x-1) 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^2-2x+2 as (x+p)(x+q)
so you have to resort to
(C + D x)/(x^2-2x+2)

1. 👍
2. 👎
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^2-2x)

(I started with known fractions and simplified, so that I would have a question that worked out)

The bottom factors to x(x+2)(x-1)

so let
(5x^2+3x+4)/(x^3+x^2-2x) = A/(x+2) + B/(x-1) + c/x

(5x^2+3x+4)/(x^3+x^2-2x)
= [Ax(x-1) + Bx(x+2) + C(x+2)(x-1)]/x(x+2)(x-1)

clearing the denominator we get:
5x^2+3x+4 = Ax(x-1) + Bx(x+2) + C(x+2)(x-1)

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^2-2x) can
be split into
3/(x+2) + 4/(x-1) - 2/x

1. 👍
2. 👎
3. Reiny. You misunderstood. And I didn't word it right.

I meant where does (Cx + D)/Something

Pop up?

1. 👍
2. 👎
4. Okay. Example.

If the Denominator is

x^4 - 2x^2 - 8 > (x-2) (x+2) (x^2+2)

Would I do A + B + C, or A + B + (Cx + D)?

1. 👍
2. 👎
5. 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?

1. 👍
2. 👎

## Similar Questions

1. ### geometry

Your class started at 12:12PM and ended at 12:50PM. What angle did the minute hand of a watch sweep through during the class?

2. ### Calculus - Find volume of cylinder

There is a cylindrical tank lying horizontally on the ground, its diameter is 8 feet, and length is 25 feet, the depth of the water currently in the tank is 2 feet. (1 gallon=231 cubic inches) How many gallons of water are in the

3. ### Math

Describe two ways to determine the larger of two fractions. A. Compare fractions by writing fractions as mixed numbers B. Compare fractions with the same denominator by comparing the numerators and compare fractions with different

4. ### Mathematics

Can someone explain to me how to solve complex fractions as if I didn't know anything about Algebra? I really need the help, thanks. :) It's not like this is the question of my homework, I just don't understand how to solve

1. ### Calc II

Perform long division on the integrand, write the proper fraction as a sum of partial fractions, and evaluate the integral: (integral of) 2y^4dy/y^3 - y^2 + y - 1 After long divison I get: (integral of)2ydy + 2(integral of)dy +

2. ### 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/((x-1)(x^2+5x+4)) 2)(3x^3-5x^2+12x+4)/(x^4-16) 3)1/(x^2 (x+1)^2 )

3. ### Calculus

How do you simplify vectors? 1)AB + BC + CD 2) BC - FE - BA + DE - DC Calculus - Steve, Tuesday, September 22, 2015 at 11:39pm AB+BC = AC so, AB+BC+CD = AD BC-DC = BC+CD = BD See if you can use that idea to rearrange +/- terms so

4. ### calculus

how to you use partial fractions to compute the integral of ax/((x^2)-bx)dx?

1. ### Maths-Integration by Partial Fraction

Use integration by partial fractions to find Integral (3x^2-x+2)/(x-1)(x^2+1) dx

2. ### calculus

what is the integral of (x^2-x+6)/(x^3-3x)? the process involves partial fractions, and the answer is supposed to include ln and arctan... i just don't know how to get there.

3. ### Binomial

Help me on this one :( Express y= (7-3x-x^2)/[((1-x)^2)(2+x)] in partial fractions. Hence, prove that if x^3 and higher powers of x may be neglected, then y=(1/8)(28+30x+41x^2) I did the first part of expressing it in partial

4. ### Math

Hi, I have to do a project on the Shell Method in my Geometry class. I have been trying to find information on that topic, but have no luck... can someone point me to the right direction as of what keyword to search for, or is