How do you express $(x-1)/(x^3 +x)$ in partial fractions?

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Answer 1 · 2016-08-14T00:06:50

$(x-1)/(x^3+x) = (x+1)/(x^2+1) - 1/x$

$(x-1)/(x^3+x) = (x-1)/(x(x^2+1))$

$(x-1)/(x(x^2+1)) = A/x + (Bx+C)/(x^2+1)$

$x-1 = A(x^2+1) + x(Bx+C)$

$x-1 = Ax^2 + A + Bx^2 + Cx$

Comparing coefficients:

$0 = A + B$

$1 = C$

$-1 = A implies B = 1$

$(x-1)/(x^3+x) = (x+1)/(x^2+1) - 1/x$

How do you express (x-1)/(x^3 +x)(x-1)/(x^3 +x) in partial fractions?