The answer is: z² .
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Given: (x÷(y÷z))÷((x÷y)÷z) ; without any specified values for the variables;
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we shall simplify.
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We have:
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(x÷(y÷z)) / ((x÷y)÷z) .
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Start with the first term; or, "numerator": (x÷(y÷z)) ;
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x ÷ (y / z) = (x / 1) * (z / y) = (x * z) / (1 *y) = [(xz) / y ]
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Then, take the second term; or "denominator":
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((x ÷ y) ÷z ) = (x / y) / z = (x / y) * (1 / z) = (x *1) / (y *z) = [x / (zy)]
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So (x÷(y÷z)) / ((x÷y)÷z) = (x÷(y÷z)) ÷ ((x÷y)÷z) =

[(xz) / y ] ÷ [x / (zy)] = [(xz) / y ] / [x / (zy)] =
[(xz) / y ] * [(zy) / x] ;
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The 2 (two) z's "cancel out" to "1" ; and
The 2 (two) y's = "cancel out" to "1" ;
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And we are left with: z * z = z² . The answer is: z² .
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3 years ago