Question

(x÷(y÷z))÷((x÷y)÷z)also the variables are not specified.

Answer 1

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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