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If xy ≠ 0 and x ≠ –y
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17 Jul 2018, 11:54
17 Jul 2018, 11:54
1
Expert Reply
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Question Stats:
87% (01:16) correct
12% (02:04) wrong based on 71 sessions
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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)\(\frac{1}{x^{9}-y^{9}}\)
(A) 1
(B) \(x^2 - y^2\)
(C) \(x^9 - y^9\)
(D) \(x^{18} - y^{18}\)
(E)\(\frac{1}{x^{9}-y^{9}}\)
Re: If xy ≠ 0 and x ≠ –y
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23 Jul 2018, 08:06
23 Jul 2018, 08:06
2
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 \((x^9 - y^9)\)
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 \((x^9 - y^9)\)
If xy 0 and x y
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15 Jun 2023, 03:26
15 Jun 2023, 03:26
1
\(\frac{x^{36} - y^{36}}{(x^{18} + y^{18})(x^9 + y^9)}\)
\(x^{36} - y^{36}\) can be rewritten as \((x^{18} + y^{18})(x^{18} - y^{18})\)
Thus, we can rewrite the original expression as
\(\frac{(x^{18} + y^{18})(x^{18} - y^{18})}{(x^{18} + y^{18})(x^9 + y^9)}\)
We can now cancel \(x^{18} + y^{18}\) in both the numerator and the denominator.
Thus we get
\(\frac{x^{18} - y^{18}}{x^9 + y^9}\)
Since \(x^{18} - y^{18}\) can be rewritten as \((x^9 + y^9 )(x^9 - y^9)\) we can rewrite the expression as
\(\frac{(x^9 + y^9 )(x^9 - y^9)}{x^9 + y^9}\)
We can cancel \((x^9 + y^9)\) in the numerator and the denominator, thus leaving us \(x^9 - y^9\)
\(x^{36} - y^{36}\) can be rewritten as \((x^{18} + y^{18})(x^{18} - y^{18})\)
Thus, we can rewrite the original expression as
\(\frac{(x^{18} + y^{18})(x^{18} - y^{18})}{(x^{18} + y^{18})(x^9 + y^9)}\)
We can now cancel \(x^{18} + y^{18}\) in both the numerator and the denominator.
Thus we get
\(\frac{x^{18} - y^{18}}{x^9 + y^9}\)
Since \(x^{18} - y^{18}\) can be rewritten as \((x^9 + y^9 )(x^9 - y^9)\) we can rewrite the expression as
\(\frac{(x^9 + y^9 )(x^9 - y^9)}{x^9 + y^9}\)
We can cancel \((x^9 + y^9)\) in the numerator and the denominator, thus leaving us \(x^9 - y^9\)
