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Question

Divide the expression
{x2+1x2+22x2x} by {x+1x2}.

A
(x2+1x2)
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B
(x1x)
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C
(x+1x)
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D
(x21x2)
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Solution

The correct option is C (x+1x)
Given: (x2+1x2+22x2x)(x+1x2)
Consider the numerator,
x2+1x2+22x2x=(x2+2+1x2)2(x+1x)
[Using identity: (a+b)2=a2+2ab+b2]

=(x+1x)22(x+1x)

=(x+1x)(x+1x2)

Therefore, (x2+1x2+22x2x)(x+1x2)=(x+1x)(x+1x2)(x+1x2)
=(x+1x)

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