How do you write the partial fraction decomposition of the rational expression #1/((x+7)(x^2+9))#?

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Answer 1 · 2015-12-14T03:40:38

#1/((x+7)(x^2+9))=(7-x)/(58(x^2+9))+1/(58(x+7))#

#1/((x+7)(x^2+9))=A/(x+7)+(Bx+C)/(x^2+9)#

#1=A(x^2+9)+(Bx+C)(x+7)#

IF #x=-7#:

#1=58A#
#A=1/58#

IF #x=0#:

#1=9/58+7C#
#C=7/58#

IF #x=7#:

#1=1+14(7B+7/58)#
#B=-1/58#

Plug in these values:

#1/((x+7)(x^2+9))=(7-x)/(58(x^2+9))+1/(58(x+7))#