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))#