Partial fraction expansion (polynomial division)

In summary, the conversation is about rationalizing an irrational partial fraction before expanding it and the process of polynomial division. The examples given involve dividing a polynomial by another and finding the remainder. The last part includes a reminder to only answer questions if one is willing to help and an example is given to demonstrate the process of polynomial division.
  • #1
seang
184
0
If we're asked to expand an irrational partial fraction, we need to rationalize it first, right? I've forgotten (well not totally) how to perform polynomial division. Here are a few examples:

1. (1000x +1000000)/(.4x + 200).

For this one I got 50000.


2. (500x + 60000)/(x+100).

For this one I got 600, is that right?

It doesn't feel like I'm doing them correctly, if my answers are wrong can somebody walk me through them?
 
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  • #2
This is fit enough even to be posted in a column even below the pre-calculus one.
Just a zer is extra in 1st and you are wrong in 2nd. Don't post such silly things anymore.
 
  • #3
vaishakh said:
This is fit enough even to be posted in a column even below the pre-calculus one.
Just a zer is extra in 1st and you are wrong in 2nd. Don't post such silly things anymore.
?
Huh? What? What kind of help is THAT? Are you threatening the OP not to post what he's not very sure about?
Please note that, IF you do not feel like answering the OP's question, DO NOT bother to answer it. Let someone else do it for YOU! :grumpy: :grumpy: :grumpy:
seang, you may want to have a look at this page.
I'll give you an example.
---------------------
Example:
[tex]\frac{2x + 5}{x + 3}[/tex]
Now first, divide 2x by x to get 2. Then multiply the divisor (i.e x + 3) by the result you just obtained (i.e 2), you will get 2x + 6.
Subtract (2x + 6) from (2x + 5) to get -1.
-1 is of the degree 0, while x + 3 is of the degree 1, and 0 < 1. Hence, -1 is the remainder, and we can stop here.
So the answer is:
[tex]\frac{2x + 5}{x + 3} = 2 - \frac{1}{x + 3}[/tex]
Can you go from here? :)
 

1. What is partial fraction expansion?

Partial fraction expansion, also known as polynomial division, is a method used to simplify complex rational expressions by breaking them into smaller, simpler fractions.

2. When is partial fraction expansion used?

Partial fraction expansion is often used in mathematics, physics, and engineering to solve integrals, differential equations, and other problems involving rational expressions.

3. How is partial fraction expansion performed?

To perform partial fraction expansion, the denominator of a rational expression is factored into irreducible polynomials, and then the coefficients of the resulting fractions are determined using a system of equations. The original expression can then be written as a sum of the simpler fractions.

4. What are the benefits of using partial fraction expansion?

Partial fraction expansion can make complex rational expressions easier to solve and can also help to identify patterns and relationships within the expression. It can also be used to find the inverse Laplace transform of a function.

5. Are there any limitations to using partial fraction expansion?

Partial fraction expansion can only be used on rational expressions, and the denominator must be factorable into irreducible polynomials. It also requires some algebraic manipulation and can be time-consuming for larger expressions.

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