How do you write the partial fraction decomposition of the rational expression $5 / (x^2 + x - 6)$ ?

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Answer 1 · 2015-12-21T09:50:58

Factorize and solve

First step is to factorize the denominator.

$Den(5/(x^2+x-6))= x^2+x-6$
$= x^2+3x-2x-6$
$= x(x+3)-2(x+3)$
$= (x+3)(x-2)$

Now the partial fractions are
$5/(x^2+x-6) = A/(x+3)+B/(x-2)$

Solve for A & B.

Multiply both sides by denominator
$A(x-2)+B(x+3)=5$

If $x=2$ we will get B

$5B=5$
$B=1$

If $x=-3$ we will get A
$-5A =5$
$A = -1$

PFs are
$5/(x^2+x-6) = 1/(x-2)-1/(x+3)$

How do you write the partial fraction decomposition of the rational expression 5 / (x^2 + x - 6)5 / (x^2 + x - 6)?