
Concept explainers
To find: The partial fraction decomposition .

Answer to Problem 36RE
x(x2+9)(x+1)=−110(x+1)+x10+910(x2+9)
Explanation of Solution
Given information: x(x2+9)(x+1)
x(x2+9)(x+1)=A(x+1)+Bx+cx2+9⇒x(x2+9)(x+1)=A(x2+9)+(Bx+c)(x+1)(x2+9)(x+1)⇒ x =A(x2+9)+(Bx+c)(x+1)
Put x=−1
A=−110
Now from equation (1)
⇒x=A(x2+9)+(Bx+c)(x+1)⇒x=−110(x2+9)+Bx2+Bx+cx+c⇒x=−x210−910+Bx2+Bx+cx+c⇒x=x2(B−110)+x(B+C)+c−910
The L.H.S and R.H.S will be equal when
B−110=0∴B=110
And
c−910=0∴c=910
And B+C=1
∴ partial fraction ,
x(x2+9)(x+1)=A(x+1)+Bx+cx2+9
⇒ x(x2+9)(x+1)=−110(x+1)+x10+910(x2+9)
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