How do you express $\frac{x^{3} + 1}{x^{2} + 4}$ $(x^3+1) / (x^2+4)$ in partial fractions?

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Answer 1 · 2016-07-29T09:41:04

$\frac{x^{3} + 1}{x^{2} + 4} = x - \frac{4 x - 1}{x^{2} + 4}$ $(x^3+1)/(x^2+4)=x-(4x-1)/(x^2+4)$

$\frac{x^{3} + 1}{x^{2} + 4} = \frac{x (x^{2} + 4)}{x^{2} + 4} + \frac{- 4 x + 1}{x^{2} + 4}$ $(x^3+1)/(x^2+4)=(x(x^2+4))/(x^2+4)+(-4x+1)/(x^2+4)$

= $x - \frac{4 x - 1}{x^{2} + 4}$ $x-(4x-1)/(x^2+4)$

How do you express x3+1x2+4(x^3+1) / (x^2+4) in partial fractions?