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

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

1 Answer

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Answer 1 · 2016-05-13T23:32:23

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

Explanation:

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

The denominator $(x^{2} + 4)$ $(x^2+4)$ has no linear factors with Real coefficients since $x^{2} + 4 \geq 4 > 0$ $x^2+4 >= 4 > 0$ for all Real values of $x$ $x$ .

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

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