Mila:
Rozłóż na ułamki proste .
| 3x | | 3x | | A | | Bx+C | |
| = |
| = |
| + |
| = |
| x3−1 | | (x−1)*(x2+x+1) | | x−1 | | x2+x+1 | |
| | A*(x2+x+1)+(Bx+C)(x−1) | |
= |
| ⇔ |
| | (x−1)*(x2+x+1 | |
3x=A*(x
2+x+1)+(Bx+C)(x−1)
1)
x=1
L=3, P=A*(1+1+1)+(B+C)*0=3A
3A=3⇔A=1
2)
x=0
L=0, P=A*1+C*(−1)=1−C
1−C=0⇔C=1
3)
x=−1
L=−3, P=A*(1−1+1)+(B*(−1)+C)*(−2)=A+2B−2C=1+2B−2
2B−1=−3⇔B=−1
| | 3x | | 1 | | −x+1 | |
4) |
| = |
| + |
| |
| | x3−1 | | x−1 | | x2+x+1 | |
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