On simplification, (x3 - y3)/[x(x + y)2 - 3xy] ÷ [y(x - y)2 + 3xy]/(x3 + y3) × (x + y)2 - (x - y)2 /(x2 - y2) is equal to:
Show answer & explanation
Correct answer: C
Explanation
The correct answer is Option 3 i.e 4.
| Understanding/Application |
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= (x3 - y3)/[x(x + y)2 - 3xy] ÷ [y(x - y)2 + 3xy]/(x3 + y3) × [{(x + y)2 - (x - y)2}/(x2 - y2)] = (x3 - y3)/[x(x + y)2 - 3xy] × [(x3 + y3)/{y(x - y)2 + 3xy}] × [{(x + y)2 - (x - y)2}/(x2 - y2)] |
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= {(x - y) (x2 + xy + y2)}/[x(x + y)2 - 3xy] × [{(x + y) (x2 - xy + y2)}/{y(x - y)2 + 3xy}] × [{(x2 + 2xy + y2) - (x2 - 2xy + y2)}/(x + y) (x - y)] = [(x2 + y2 + xy)/{x(x2 -xy + y2}] × [(x2 + y2 - xy)/{y(x2 + y2 + xy}] × 4xy = 4 |