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Question

If x2+x+1x2+2x+1=A+Bx+1+C(x+1)2 then A−B=

A
4C
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B
4C+1
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C
3C
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D
2C
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Solution

The correct option is C 2C
Given, x2+x+1(x+1)2=A+B(x+1)+C(x+1)2
x2+x+1(x+1)2=A(x+1)2+B(x+1)+C(x+1)2
x2+x+1=A(x+1)2+B(x+1)+C
Let us put x=2
3c=AB
AB=2
and
f(1)=c=1
So AB=2C

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