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Math Help - Please show working to express these in partial fractions

  1. #1
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    Exclamation Please show working to express these in partial fractions

    Express in partial fractions:


    a) (3x + 1) / (x + 1)^2


    b) (x^2 + 7x + 2) / (1 + x^2)(2 - x)
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  2. #2
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    Quote Originally Posted by malteseboy View Post
    Express in partial fractions:


    a) (3x + 1) / (x + 1)^2


    b) (x^2 + 7x + 2) / (1 + x^2)(2 - x)

    \frac{3x+1}{(x+1)^2} = \frac{A}{x+1} + \frac{B}{(x+1)^2}


    \frac{x^2+7x+2}{(1+x^2)(2-x)} = \frac{Ax+B}{1+x^2} + \frac{C}{2-x}
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  3. #3
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    Quote Originally Posted by malteseboy View Post
    Express in partial fractions:


    a) (3x + 1) / (x + 1)^2


    b) (x^2 + 7x + 2) / (1 + x^2)(2 - x)
    a)
    \frac {3x + 1} {(x + 1)^2} (it's the repeated factor type) so
    \frac {3x + 1} {(x + 1)^2}=\frac {A}{x+1}+\frac {B}{(x+1)^2}
    \frac {3x + 1} {(x + 1)^2}=\frac {A(x+1)+B}{(x+1)^2}
    you can cancel the denominator,
    so you have
    3x + 1=A(x+1)+B
    you just have to find the value for A and B and then change A and B from this eq... \frac {A}{x+1}+\frac {B}{(x+1)^2}

    ....hope it help.....
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