How do you write the partial fraction decomposition of the rational expression $\frac{x - 5}{{(x - 2)}^{2}}$ $( x-5)/(x-2)^2$ ?

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How do you write the partial fraction decomposition of the rational expression $\frac{x - 5}{{(x - 2)}^{2}}$ $( x-5)/(x-2)^2$ ?

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Answer 1 · 2016-06-12T15:02:25

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

Explanation:

$\frac{x - 5}{{(x - 2)}^{2}}$ $(x-5)/(x-2)^2$
$= \frac{(x - 2) - 3}{{(x - 2)}^{2}}$ $= ((x-2)-3)/(x-2)^2$
$= \frac{x - 2}{{(x - 2)}^{2}} - \frac{3}{{(x - 2)}^{2}}$ $= (x-2)/(x-2)^2 -3/(x-2)^2$
$= \frac{1}{x - 2} - \frac{3}{{(x - 2)}^{2}}$ $= 1/(x-2) - 3/(x-2)^2$

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How do you write the partial fraction decomposition of the rational expression $\frac{x - 5}{{(x - 2)}^{2}}$ $( x-5)/(x-2)^2$ ?

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How do you write the partial fraction decomposition of the rational expression $\frac{x - 5}{{(x - 2)}^{2}}$ $( x-5)/(x-2)^2$ ?