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If xy 0 and x -y, =
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sandy
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Joined: 07 Jun 2014
Posts: 4805
GRE 1: Q167 V156
WE:Business Development (Energy and Utilities)
If xy 0 and x -y, = [#permalink] New post  19 May 2018, 15:13
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If \(xy \neq 0\) and \(x \neq -y\),\(\frac{x^{36}-y^{36}}{(x^{18}+y^{18})(x^{9}+y^{9})}\) =

(A) \(1\)
(B) \(x^2 - y^2\)
(C) \(x^9 - y^9\)
(D) \(x^{18} - y^{18}\)
(E) \(\frac{1}{x^9 - y^9}\)
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mohan514
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GRE 1: Q165 V156
Re: If xy 0 and x -y, = [#permalink] New post  21 May 2018, 21:24
1
(a+b)*(a-b)= a^2-b^2.
Using this formula to further solve the above equation leaves us with option C
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cristianrosales
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Re: If xy 0 and x -y, = [#permalink] New post  27 Sep 2020, 11:33
Can someone explain this in more detail? I'm not sure what to do on this one :)
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Re: If xy 0 and x -y, = [#permalink] New post  03 Oct 2020, 10:23
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sandy wrote:
If \(xy \neq 0\) and \(x \neq -y\),\(\frac{x^{36}-y^{36}}{(x^{18}+y^{18})(x^{9}+y^{9})}\) =

(A) \(1\)
(B) \(x^2 - y^2\)
(C) \(x^9 - y^9\)
(D) \(x^{18} - y^{18}\)
(E) \(\frac{1}{x^9 - y^9}\)


\(\frac{x^{36}-y^{36}}{(x^{18}+y^{18})(x^{9}+y^{9})}=\frac{(x^{18}+y^{18})(x^{18}-y^{18})}{(x^{18}+y^{18})(x^{9}+y^{9})}\)

\(=\frac{(x^{18}-y^{18})}{(x^{9}+y^{9})}\)

\(=\frac{(x^{9}+y^{9})(x^{9}-y^{9})}{(x^{9}+y^{9})}\)

\(=x^{9}-y^{9}\)

Answer: C
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