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Question

If 1x4+x2+1=Ax+Bx2+x+1+Cx+Dx2−x+1, then C+D=

A
-1
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B
1
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C
2
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D
0
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Solution

The correct option is D 0
Ax+B(x2+1)+x+Cx+D(x2+1)x
=Ax(x2+1x)+B(x2+1x)+Cx(x2+1+x)+D(x2+1+x)(x2+1)2x2
=x3(A+C)+x2(C+D+BA)+x(AB+C+D)+B+Dx4+x2+1
Comparing with
1x4+x2+1
Gives us
A+C=0, B+D+CA=0, A+C+DB=0 and B+D=1
Consider the equations
B+D+CA+0 and
A+C+DB=0
Adding both gives us
2(D+C)=0
D+C=0

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