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 S_David Feb4-12 11:01 PM

Partial Fraction

Hello,

Is there any general formula for the partial fraction of the following function:

$$\frac{1}{(ax_1+1)(ax_2+1)\cdots (ax_L+1)}$$

I can work for L=3, but it get involved for larger L!!

 coelho Feb5-12 04:06 AM

Re: Partial Fraction

Ok... from what ive understood, you want write

$$\frac{1}{(ax_1+1)(ax_2+1)\cdots(ax_L+1)}$$

as

$$\frac{c_1}{ax_1+1}+\frac{c_2}{ax_2+1}+\cdots+\frac{c_L}{ax_L+1}$$

where the c's are constants. My question is, what is the variable the c's must be independent of? a or x?

 S_David Feb5-12 09:55 AM

Re: Partial Fraction

Quote:
 Quote by coelho (Post 3746152) Ok... from what ive understood, you want write $$\frac{1}{(ax_1+1)(ax_2+1)\cdots(ax_L+1)}$$ as $$\frac{c_1}{ax_1+1}+\frac{c_2}{ax_2+1}+\cdots+\frac{c_L}{ax_L+1}$$ where the c's are constants. My question is, what is the variable the c's must be independent of? a or x?
a is a constant, and x's are the variables.

 mathman Feb5-12 03:34 PM

Re: Partial Fraction

Quote:
 Quote by coelho (Post 3746152) Ok... from what ive understood, you want write $$\frac{1}{(ax_1+1)(ax_2+1)\cdots(ax_L+1)}$$ as $$\frac{c_1}{ax_1+1}+\frac{c_2}{ax_2+1}+\cdots+\frac{c_L}{ax_L+1}$$ where the c's are constants. My question is, what is the variable the c's must be independent of? a or x?
Problems involving partial fractions usually have one variable and many constants. From the appearance of your expression, I assume a is the variable and the x's are constants. In that case the c's will be determined by the x's.

 S_David Feb5-12 04:24 PM

Re: Partial Fraction

Quote:
 Quote by mathman (Post 3747156) Problems involving partial fractions usually have one variable and many constants. From the appearance of your expression, I assume a is the variable and the x's are constants. In that case the c's will be determined by the x's.
yes, right. a is the variable and x's are the constants. I got the general solution expression.

Thanks

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