Math grade 12
posted by Rass on .
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(x3)(x+2)(x1)^2(x^2+1)^2(x^21)^3

Look how your expression turned out.
Use brackets and such symbols as / for division to type your expression. 
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(x3)(x+2)(x1)^2(x^2+1)^2(x^21)^3 
Can anyone please help me?

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%28x3%29%28x%2B2%29%28x1%29%5E2%28x%5E2%2B1%29%5E2%28x%5E21%29%5E3%29 
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 :)

Do you realize the number of cases you can have
e.g.
A/x + B/x^2 + C/x^3 + D/(x3) + 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(x3)(x+2)(x^21)^3 )
can you see the absurdity of this question?
There would be 12 different factors, which would make 2^12  1 or 4095 subsets 
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?

10bb+1