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    I don't know if this is going to make sense but I will try my best to explain it anyways.
    We started studying integration with partial fractions today and my teacher said that when the fraction has an (x) with the same power on both the numerator and denominator, you have to do long division and then use the normal A/(x+..) B/(X+..) method to integrate it. Is this true?

    For example:

    x^2/ x^2 + 4

    would I have to use long division before working with it or can I just write it out as:

    x^2 = 1 + A/x+2 + B/x-2

    and then start solving...


    sorry if it didn't make sense but I don't know how else to explain it!! Thank you in advance
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    (Original post by parsyyy)
    I don't know if this is going to make sense but I will try my best to explain it anyways.
    We started studying integration with partial fractions today and my teacher said that when the fraction has an (x) with the same power on both the numerator and denominator, you have to do long division and then use the normal A/(x+..) B/(X+..) method to integrate it. Is this true?

    For example:

    x^2/ x^2 + 4

    would I have to use long division before working with it or can I just write it out as:

    x^2 = 1 + A/x+2 + B/x-2

    and then start solving...


    sorry if it didn't make sense but I don't know how else to explain it!! Thank you in advance
    Yes. If the power of the numerator is equal to or greater than the power of the denominator, you should do long division first and then split the fraction into partial fractions.
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    (Original post by Chlorophile)
    Yes. If the power of the numerator is equal to or greater than the power of the denominator, you should do long division first and then split the fraction into partial fractions.
    thank you! what about if the denominator has already been factorised?
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    (Original post by parsyyy)
    thank you! what about if the denominator has already been factorised?
    Then you need to unfactorise it. As far as I know, the best way to do these questions when the numerator is greater than the denominator is long division followed by partial fractions followed by integration.
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    (Original post by Chlorophile)
    Then you need to unfactorise it. As far as I know, the best way to do these questions when the numerator is greater than the denominator is long division followed by partial fractions followed by integration.
    alright thank you!
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    (Original post by parsyyy)
    alright thank you!
    Your welcome
 
 
 
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