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

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

1 Answer

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Answer 1 · 2016-05-29T12:36:24

$\frac{x^{2} + 2}{x + 2} = x - 2 + \frac{6}{x + 2}$ $(x^2+2)/(x+2)= x-2+6/(x+2)$

Explanation:

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

$= \frac{x^{2} + 2 x - 2 x - 4 + 6}{x + 2}$ $= (x^2+2x-2x-4+6)/(x+2)$

$= \frac{x (x + 2) - 2 (x + 2) + 6}{x + 2}$ $= (x(x+2)-2(x+2)+6)/(x+2)$

$= x - 2 + \frac{6}{x + 2}$ $= x-2+6/(x+2)$

If you prefer, you can long divide the coefficients like this:

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Notice the $0$ $0$ in the dividend to stand for the missing $x$ $x$ term in the numerator.

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

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Explanation:

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