(x+3)(x2−x+1)x2+x+1= x+3A+x2−x+1Bx+C
x2+x+1=A(x2−x+1)+(Bx+C)(x+3)
Equating coefficients, we get:
1=A+B (1)
1=−A+3B+C (2)
1=A+3C (3)
Substituting (1) into (2) gives
1=−A+3(1−A)+C=−4A+C+3 (4)
Now let’s substitute (3) into (4)
1=−4(1−3C)+C+3=13C−1
C=132
A=1−3C=1−136=137
B=1−A=1−137=136
(x+3)(x2−x+1)x2+x+1=131x+37+131x2−x+16x+2
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