Write the partial fraction decomposition for the rational expression \frac{3x^{2}-2x-1}{x(x+1)^{2}(x^{2}+4)^{2}}

osteoblogda 2021-12-16 Answered
Write the partial fraction decomposition for the rational expression
3x22x1x(x+1)2(x2+4)2
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Expert Answer

censoratojk
Answered 2021-12-17 Author has 46 answers
Solving: Given 3x22x1x(x+1)2(x2+4)2
Write the partial fraction decomposition for the rational expression
Using partial fraction rule
ax+b(x+a)2(x+b)=A(x+a)+B(x+a)2+C(x+b)
ax+b{x2+a2)(x+b)}}=Ax+bx2+a2+C(x+b)
Step 2
Then for are given 3x22x1x(x+1)2(x2+4)2
3x22x1x(x+1)2(x2+4)2=Ax+B(x+1)+C(x+1)2+Dx+E(x2+4)+Fx+G(x2+4)2
Hence write the partial fraction dicompositien for the rational expression
3x22x1x(x+1)2(x2+4)2=Ax+B(x+1)+C(x+1)2+Dx+E(x2+4)+Fx+G(x2+4)2
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Dawn Neal
Answered 2021-12-18 Author has 35 answers
Step 1
Given:
3x22x1x(x+1)2(x2+4)2
(x+1)2=x2+2x+1
=3x22x1x(x2+2x+1)(x2+4)2
(x2+4)2=x4+8x2+16
3x22x1x(x2+2x+1)(x4+8x2+16)
Expand
(x2+2x+1)(x4+8x2+16):x7+2x6+9x5+16x4+24x3+32x2+16x
=3x22x1x7+2x6+9x5+16x4+24x3+32x2+16x
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