Partial Fractions Watch

badeninc
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#1
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#1
Hi, 1st question of A2 Maths.

Split the following into partial fractions:

25/(x^3 -3x - 4)

Working:

5/(x-4) +/- 5/(x+1)

How do I know weather the symbol in between is a plus or a minus the correct symbol is a minus
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sussexy
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I assume that's supposed to be an x^2 instead of an x^3...

Well basically you say that

\frac{25}{x^2 - 3x - 4} = \frac{A}{x - 4} + \frac{B}{x + 1}

Then you get a common denominator on the right hand side (which of course will be the same as the denominator on your left).

So 25 = A(x + 1) + B(x - 4)

25 + 0x = Ax + Bx + A - 4B

Ax + Bx = 0x

25 = A - 4B

Can you figure it out from here?
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badeninc
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Yes I understand all that so basically if A is a -ve value the sign in between is -ve but we write A as being positive
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Adjective
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Well, how have you got to  \frac{5}{x-4} \pm \frac{5}{x+1} ? (I assume you mean x^2 in the denominator rather than x^3).

You've presumably got to  25 = A(x+1) + B(x-4) - how do you find A and B from here?

EDIT: Okay, so I was a tad slow...

(Original post by badeninc)
Yes I understand all that so basically if A is a -ve value the sign in between is -ve but we write A as being positive
If you find a partial fraction's numerator to be negative, say, -2, then you will have something like  \frac{A}{blah_1} + \frac{-2}{blah_2} - which equals  \frac{A}{blah_1} - \frac{2}{blah_2} . I think you've got the right idea.
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sussexy
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(Original post by badeninc)
Yes I understand all that so basically if A is a -ve value the sign in between is -ve but we write A as being positive
I don't get what you mean.

You've said that \frac{25}{x^2 - 3x - 4} = \frac{A}{x - 4} + \frac{B}{x + 1} and you know how to find values for A and B... so just sub them back into \frac{A}{x - 4} + \frac{B}{x + 1}.
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badeninc
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Adje if thats the right way it makes sense just how I imagined it to be
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...bored
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#7
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If B for instance is negative then you would put the partial fraction on the left (minus) the partial fraction for the constant B. I can't explain it properly m sorry"
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