1. ## partial fraction query

hi - I've got an intergral to solve but when seperating this fraction get a different answer to my Maple solution. Take a look and show me where i'm going wrong because i'm stumped!

$\frac{x+2}{1-4x^2}$
i) $=\frac{x+2}{(1-2x)(1+2x)}$
ii) $=\frac{5}{4(1-2x)} + \frac{3}{4(1+2x)}$

but my program tells me its $=\frac{-5}{4(1-2x)} + \frac{3}{4(1+2x)}$

I can't see why the negative sign is introduced. Any ideas??

Cheers, F

2. ## Re: partial fraction query

Hello, FelixHelix!

Maple is wrong . . . I have no idea why.

3. ## Re: partial fraction query

Edit: Beaten to it.

$\frac{x+2}{(1-2x)(1+2x)}=\frac{A}{1-2x}+\frac{B}{1+2x}$

$\rightarrow A(1+2x)+B(1-2x)=x+2$

Let $x=\frac{1}{2}$

$2A=\frac{5}{2}$

$A=\frac{5}{4}$

Let $x=\frac{-1}{2}$

$2B=\frac{3}{2}$

$B=\frac{3}{4}$

As far as I can tell there isn't an error with your work. Wolfram Alpha agrees in this respect, but not this one, so I wonder whether there's some sort of problem with their Gaussian Elimination or something.

4. ## Re: partial fraction query

Originally Posted by FelixHelix
hi - I've got an intergral to solve but when seperating this fraction get a different answer to my Maple solution. Take a look and show me where i'm going wrong because i'm stumped!
I wonder if you are reading Maple correctly?
The program gives me $\frac{-5}{4(2x-1)}+\frac{3}{4(2x+1)}$.

But that is the same as $\frac{5}{4(1-2x)}+\frac{3}{4(1+2x)}$

5. ## Re: partial fraction query

Reading the given answer carefully is something I'll have to pay more attention to.

6. ## Re: partial fraction query

Originally Posted by Plato
I wonder if you are reading Maple correctly?
The program gives me $\frac{-5}{4(2x-1)}+\frac{3}{4(2x+1)}$.

But that is the same as $\frac{5}{4(1-2x)}+\frac{3}{4(1+2x)}$

You're absolutely right Plato! Thanks for this - I'll take care in reading off in the future...

All the best