x / (x² + 1) (x - 1) (x + 2) solve into partial fractions
Answers
How do I solve this into a partial fraction x²+1/(x-1)²(x²+2x+2)?
Reducing Fractions and/or Factorizations is always a Discretion, as truly, the Fraction and Numbers are oft supplied as they are to provide an Information.
Explanation
Although there is no proof for or against this due the actual vagueness of: No =□ was supplied to actually Infer, let place this into an Informative Perspective, and in a Real life circumstance, such of the like would not even place on your desk without scrutiny, except if there was an undertrained personnel gathering or journalling infos, and yourself were the Super
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x2+1(x−1)2(x2+2x+2)=Ax−1+B(x−1)2+Cx+Dx2+2x+2
x2+1(x−1)2(x2+2x+2)=A(x−1)(x2+2x+2)+B(x2+2x+2)+(Cx+D)(x−1)2(x−1)2(x2+2x+2)
x2+1=A(x−1)(x2+2x+2)+B(x2+2x+2)+(Cx+D)(x−1)2
x2+1=A(x3+x2−2)+B(x2+2x+2)+(Cx+D)(x2−2x+1)
x2+1=Ax3+Ax2−2A+Bx2+2Bx+2B+Cx3+(D−2C)x2+(C−2D)x+D
x2+1=(A+C)x3+(A+B−2C+D)x2+(2B+C−2D)x+(−2A+2B+D)
A+C=0⟹A=−C
A+B−2C+D=1⟹B−3C+D=1
2B+C−2D=0
−2A+2B+D=1⟹2B+2C+D=1
(2B+2C+D)−(2B+C−2D)=1−0⟹C+3D=1
2(B−3C+D)−(2B+C−2D)=2(1)−0⟹−7C+4D=2
7(C+3D)+(−7C+4D)=7(1)+2⟹25D=9⟹D=925
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Step-by-step explanation:
x ³+ x2 ( x²+2 x - x- 2)
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