Posted by **Rass** on Sunday, January 1, 2012 at 8:40pm.

write the partial fraction decomposition of the following rational expression ( hint: binomial expansion with Pascal triangle can be used to expand binomials. technology may be used to solve large systems using matrices or determinants)

4

------------------------------------- x^3(x-3)(x+2)(x-1)^2(x^2+1)^2(x^2-1)^3

- check typing - Math grade 12 -
**Reiny**, Sunday, January 1, 2012 at 8:43pm
Look how your expression turned out.

Use brackets and such symbols as / for division to type your expression.

- Math grade 12 -
**Rass**, Sunday, January 1, 2012 at 8:48pm
this better?

write the partial fraction

decomposition of the following rational expression ( hint: binomial expansion with Pascal triangle can be used to expand binomials. technology may be used to solve large systems using matrices or determinants)

4/x^3(x-3)(x+2)(x-1)^2(x^2+1)^2(x^2-1)^3

- Math grade 12 -
**Rass**, Sunday, January 1, 2012 at 9:00pm
Can anyone please help me?

- Math grade 12 -
**Reiny**, Sunday, January 1, 2012 at 9:00pm
Are you serious?

Is this an actual question from a textbook?

Even Wolfram had a hemorrhage trying to do that one

Look at the "partial fraction expansion"

http://www.wolframalpha.com/input/?i=4%2F%28x%5E3%28x-3%29%28x%2B2%29%28x-1%29%5E2%28x%5E2%2B1%29%5E2%28x%5E2-1%29%5E3%29

- Math grade 12 -
**Rass**, Sunday, January 1, 2012 at 9:04pm
Yes I am very serious. My math teacher must be playing a sick joke with us. He said it would hurt our brain. I guess he just wants us to know that there are such problems as this one that exists. thank you for your help though :)

- Math grade 12 -
**Reiny**, Sunday, January 1, 2012 at 9:12pm
Do you realize the number of cases you can have

e.g.

A/x + B/x^2 + C/x^3 + D/(x-3) + E/(x+2) + F(x^2+1) + G/(x^2+1)^2 + ........

and we should not forget such fractions as

?/(x(x^2+1)) or ?/(x(x-3)(x+2)(x^2-1)^3 )

can you see the absurdity of this question?

There would be 12 different factors, which would make 2^12 - 1 or 4095 subsets

- Math grade 12 -
**Rass**, Sunday, January 1, 2012 at 9:27pm
I see what you're saying. Thank you very much. there is no way to do this with binomial expansion though with the pascal triangle or it's still impoosibly long?

- Math grade 12 -
**joe**, Tuesday, January 3, 2012 at 7:31pm
10b-b+1

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