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    Hi. Can someone please help me with this question... Express (x^2 + 2x) / (x - 2)(x^2 + 4) in partial fractions.
    I know that since the denominator has an irreducible quadratic, I need to equate to [A / (x - 2)] + [(Bx + C) / (x^2 + 4)] and I know how to do the method to get values for A, B and C. I am getting A=1, B=0 and C=2 (and know to sub these in for the final answer), but I'm not sure that it is right, especially the B=0 part, as I have never seen one of this form with B=0 and my teacher said there should be an x term in the second fraction's numerator. Any help would be great, thanks
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    (Original post by Labrador99)
    Hi. Can someone please help me with this question... Express (x^2 + 2x) / (x - 2)(x^2 + 4) in partial fractions.
    I know that since the denominator has an irreducible quadratic, I need to equate to [A / (x - 2)] + [(Bx + C) / (x^2 + 4)] and I know how to do the method to get values for A, B and C. I am getting A=1, B=0 and C=2 (and know to sub these in for the final answer), but I'm not sure that it is right, especially the B=0 part, as I have never seen one of this form with B=0 and my teacher said there should be an x term in the second fraction's numerator. Any help would be great, thanks
    You have the correct values for A, B and C.
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    (Original post by B_9710)
    You have the correct values for A, B and C.
    Thank you very much
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    (Original post by Labrador99)
    Thank you very much
    An easy way to check is to plug a few different values of x into the expression  \displaystyle \frac{x^2+2x}{(x-2)(x^2+4)} -\left (\frac{1}{x-2}+\frac{2}{x^2+4} \right ) and you should get 0 showing that they're identical.
 
 
 
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