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What does partial-fraction decomposition mean?
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How do you write the partial fraction decomposition of the rational expression $\frac{1}{(x + 6) (x^{2} + 3)}$ $1/((x+6)(x^2+3))$ ?

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Answer 1 · 2017-12-07T18:31:31

$\frac{x}{{(x^{2} + 16)}^{2}} - \frac{16 x}{{(x^{2} + 16)}^{3}}$ $x/(x^2+16)^2-(16x)/(x^2+16)^3$

$\frac{x^{3}}{{(x^{2} + 16)}^{3}}$ $x^3/(x^2+16)^3$

= $\frac{x^{3} + 16 x - 16 x}{{(x^{2} + 16)}^{3}}$ $(x^3+16x-16x)/(x^2+16)^3$

= $\frac{x}{{(x^{2} + 16)}^{2}} - \frac{16 x}{{(x^{2} + 16)}^{3}}$ $x/(x^2+16)^2-(16x)/(x^2+16)^3$