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Question

If x2+1x4+x2+1=Ax+Bx2+x+1+Cx+Dx2−x+1thenA−C=

A
B+D
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B
B+D1
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C
B+D+1
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D
B+D+2
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Solution

The correct option is D B+D1
LHS=x2+1x4+x2+1;RHS=(Ax+B)(x2x+1)
+(Cx+D)(x2+x+1)x4+x2+1
LHS=RHS
Comparing the co-efficients of powers of x.
Co-efficients of x3 we get
A+C=O(1)
comparing x2 we get A+B+C+D=1(2)
from (2) re arrarainging terms we get
AC=B+D1

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