Maths

Resolve into partial fractions:

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

Can anyone please help me out?

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  1. 8/x^3

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  2. (x+3)(x+1)/[x(x^2+x+1)] =

    A/x + (B + C x)/(x^2 + x + 1)

    To find A multiply both sides by x and take the limit x --> 0:

    A = 3

    To find B and C you can just move the A/x term to the other side and simplify:

    (B + C x)/(x^2 + x + 1) =

    (x+3)(x+1)/[x(x^2+x+1)] - 3/x =

    (x^2 + 4x + 3 - 3 x^2 - 3 x - 3)/[x(x^2+x+1)] =

    (-2x^2 + x)/[x(x^2+x+1)] =

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

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