How do you write the partial fraction decomposition of the rational expression $(x + 2) /( x(x - 4))$ ?

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Answer 1 · 2015-12-14T21:06:23

$(x+2)/(x(x-4))=3/(2(x-4))-1/(2x)$

$(x+2)/(x(x-4))=A/x+B/(x-4)$

$x+2=A(x-4)+Bx$

IF $x=0$ :

$2=-4A$
$A=-1/2$

IF $x=4$ :

$6=4B$
$B=3/2$

Therefore:

$(x+2)/(x(x-4))=3/(2(x-4))-1/(2x)$

How do you write the partial fraction decomposition of the rational expression (x + 2) /( x(x - 4))(x + 2) /( x(x - 4))?