How do you write the partial fraction decomposition of the rational expression $( x-2 ) / (x^2 + 4x + 3)$ ?

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Answer 1 · 2015-12-16T15:58:33

$5/(2(x+3))-3/(2(x+1))$

Factor the denominator.

$(x-2)/((x+1)(x+3))=A/(x+1)+B/(x+3)$

$x-2=A(x+3)+B(x+1)$

If $x=-3$ :

$-3-2=B(-2)$
$B=5/2$

If $x=-1$ :

$-1-2=A(2)$
$A=-3/2$

Plug the values back in.

$(x-2)/(x^2+4x+3)=5/(2(x+3))-3/(2(x+1))$

How do you write the partial fraction decomposition of the rational expression ( x-2 ) / (x^2 + 4x + 3) ( x-2 ) / (x^2 + 4x + 3)?