c4: quick question re: partial fractions

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marcsaccount
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#1
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#1
Hi,

If I have a fraction, say \frac{1}{u(u-1)} because I have a squared term in the denominator, would the fraction be equivalent to  \frac{A}{u} + \frac{B}{u^2} - \frac{C}{u} ?

Is the above the best way (only way?) to do it?

Thanks
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atsruser
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#2
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(Original post by marcsaccount)
Hi,

If I have a fraction, say \frac{1}{u(u-1)} because I have a squared term in the denominator, would the fraction be equivalent to  \frac{A}{u} + \frac{B}{u^2} - \frac{C}{u} ?

Is the above the best way (only way?) to do it?

Thanks
That doesn't give you the right denominator. You only have linear terms so the partial fractions are \frac{A}{u} + \frac{B}{u-1}

If we combine your terms we get \frac{A}{u} + \frac{B}{u^2} - \frac{C}{u} = \frac{D}{u} + \frac{B}{u^2} = \frac{Du+B}{u^2} where D=A-B
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marcsaccount
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#3
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#3
(Original post by atsruser)
That doesn't give you the right denominator. You only have linear terms so the partial fractions are \frac{A}{u} + \frac{B}{u-1}

If we combine your terms we get \frac{A}{u} + \frac{B}{u^2} - \frac{C}{u} = \frac{D}{u} + \frac{B}{u^2} = \frac{Du+B}{u^2} where D=A-B

Hi - thanks for your help. I thought it was a repeated term because if the bracket is expanded the denominator would be  u^2 - u , but this isn't a repeated term?
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BananaPie
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#4
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#4
It would be repeated if it was u(u-1)^2 as you see the (u-1) is repeated twice due to the second order.
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atsruser
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#5
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(Original post by marcsaccount)
Hi - thanks for your help. I thought it was a repeated term because if the bracket is expanded the denominator would be  u^2 - u , but this isn't a repeated term?
You are looking for terms that are multiplied in the denominator, not added or subtracted, due to the way fractions with different denominators are added - think about finding a common denominator when adding fractions:

\frac{a}{x} + \frac{b}{y} = \frac{ay}{xy} + \frac{xb}{xy} = \frac{ay+bx}{xy}

Note that we multiplied, not added, the denominators.
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marcsaccount
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#6
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#6
OK, it's clear now, thanks for your help
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