The answer is: z² . __________________________ Given: <span>(x÷(y÷z))÷((x÷y)÷z) ; without any specified values for the variables; _______________________ we shall simplify. ___________________ We have: __________ </span>(x÷(y÷z)) / ((x÷y)÷z) . _____________________________________ Start with the first term; or, "numerator": (x÷(y÷z)) ; _____________________________________ x ÷ (y / z) = (x / 1) * (z / y) = (x * z) / (1 *y) = [(xz) / y ] _____________________________________ Then, take the second term; or "denominator": _____________________________________ ((x ÷ y) ÷z ) = (x / y) / z = (x / y) * (1 / z) = (x *1) / (y *z) = [x / (zy)] _________________________________________ 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] ; _______________________________________ The 2 (two) z's "cancel out" to "1" ; and The 2 (two) y's = "cancel out" to "1" ; ______________________________________________ And we are left with: z * z = z² . The answer is: z² . ______________________________________________
You know the product will be greater than the two factors because multiplication always makes the numbers greater. So 2x12 is 24 and that is greater than the two factors
