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Question

Simplify:
[x3+y3(xy)2+3xy]÷[(x+y)23xyx3y3]×xyx2y2

A
1
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B
2xy
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C
xy
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D
None of these
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Solution

The correct option is D xy
x3+y3(xy)2+3xy÷(x+y)23xyx3y3×xyx2y2

=(x+y)(x2+y2xy)(x2+y22xy+3xy)÷x2+y2+2xy3xy(xy)(x2+y2+xy)×xy(xy)(x+y)

(x+y)(x2+y2xy)(x2+y2+xy)×(xy)(x2+y2+xy)(x2+y2xy)×xy(xy)(x+y)

=xy

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