# Math grade 12

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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 -

Look how your expression turned out.

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

• Math grade 12 -

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 -

• Math grade 12 -

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 -

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 -

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 -

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 -

10b-b+1

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