How do you write the partial fraction decomposition of the rational expression $(9x) / (x^2 + 2x - 8)$ ?

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Answer 1 · 2015-12-21T04:53:46

$6/(x+4)+3/(x-2)$

Factor the denominator.

$(9x)/((x+4)(x-2))=A/(x+4)+B/(x-2)$

Simplify.

$9x=A(x-2)+B(x+4)$

Plug in $-4$ for $x$ :

$9(-4)=A(-4-2)$
$A=6$

Plug in $2$ for $x$ :

$9(2)=B(2+4)$
$B=3$

Plug these values into the original statement.

$(9x)/(x^2+2x-8)=6/(x+4)+3/(x-2)$

How do you write the partial fraction decomposition of the rational expression (9x) / (x^2 + 2x - 8) (9x) / (x^2 + 2x - 8)?