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GRE Prep Club Legend  Joined: 07 Jun 2014
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GRE 1: Q167 V156 WE: Business Development (Energy and Utilities)
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If xy ≠ 0 and x ≠ –y [#permalink]
Expert's post 00:00

Question Stats: 83% (01:32) correct 16% (00:00) wrong based on 6 sessions
If xy ≠ 0 and x ≠ –y,$$\frac{x^{36}-y^{36}}{(x^{18}+y^{18})(x^{9}+y^{9})}$$

(A) 1
(B) $$x^2 - y^2$$
(C) $$x^9 - y^9$$
(D) $$x^{18} - y^{18}$$
(E)$$\frac{1}{x^{9}-y^{9}}$$
[Reveal] Spoiler: OA

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Director  Joined: 07 Jan 2018
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Kudos [?]: 546 , given: 88

Re: If xy ≠ 0 and x ≠ –y [#permalink]
looking at the question stem. The numerator can be simplified to the form $$(x-y)(x+y)$$ because it is in the form $$x^2 - y^2$$
Hence the fraction becomes $$\frac{(x^1^8 + y^1^8)(x^1^8 - y^1^8)}{(x^1^8 + y^1^8)(x^9 + y^9)}$$
we can cancel $$(x^1^8 + y^1^8)$$ from both numerator and denominator.
Leaving $$\frac{(x^1^8 - y^1^8)}{(x^9 + y^9)}$$

numerator can again be simplified

$$\frac{(x^9 - y^9)(x^9 + y^9)}{(x^9 + y^9)}$$
we can again cancel $$(x^9 + y^9)$$
finally, leaving $$(x^9 - y^9)$$
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This is my response to the question and may be incorrect. Feel free to rectify any mistakes Re: If xy ≠ 0 and x ≠ –y   [#permalink] 23 Jul 2018, 08:06
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