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# Partial Fraction Question C4 watch

1. (1+2x)/ (x-2)(x^2 + 1)

I've tried to break it up the normal way-->

1+2x = A/(x-2) + B(X^2 +1)

But on working backwards on the answer I get, I cannot get back to the original fraction, so I don't think this is correct.

Is there another method to do here?

Thanks.
2. Hi ViolinFirl.

Now that is very nearly correct, but theres one error in you method. Your dealing with a non-linear factor in the denominator ie the x^2 + 1, now when you have this in partial fractions you need to do something slightly different, like this:

You see how there is a linear factor in the numerator of the second fraction on the RHS. hopefully this will help
3. You're trying to get your fraction into fractions of the form , right? But notice that x^2 + 1 has degree 2 (i.e. has an x^2 term in it), so you should actually be looking for something of the form - in general, if the denominator has degree n, your numerator might well have anything up to degree n-1. If there was a cubic on the bottom, you'd need to put a quadratic on the top, etc.

Edit: snap.
4. (Original post by ViolinGirl)
(1+2x)/ (x-2)(x^2 + 1)

I've tried to break it up the normal way-->

1+2x = A/(x-2) + B(X^2 +1)

But on working backwards on the answer I get, I cannot get back to the original fraction, so I don't think this is correct.

Is there another method to do here?

Thanks.

5. (1+2x)/ (x-2)(x^2 + 1)

I've tried to break it up the normal way-->

1+2x = A/(x-2) + B(X^2 +1)

But on working backwards on the answer I get, I cannot get back to the original fraction, so I don't think this is correct.

Is there another method to do here?

Thanks.
The expression you want is

This is because the x^2 term means there is a quadratic factor in the denominator, so you need more than just B.

Check here (bottom of page) for a better explanation than mine!

http://www.mathsrevision.net/alevel/pages.php?page=94
6. Thanks to you both!

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