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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