If \(x = \frac{2}{3}\) and \(y = \frac{3}{4}\), then a rational num

1.	If \(x = \frac{2}{3}\) and \(y = \frac{3}{4}\), then a rational number between (x - y)-1 and (x-1 - y-1) is1. \(-\frac{71}{12}\)2. \(\frac{1}{6}\)3. \(\frac{2}{3}\)4. \(-\frac{71}{2}\)
Answer» Correct Answer - Option 1 : \(-\frac{71}{12}\) Calculation : x = 2/3 and y = 3/4 x - y = 2/3 - 3/4 = (8 - 9)/12 = -1/12 ∴ (x - y)^-1 = -12 x^-1 = 3/2 and y^-1 = 4/3 x^-1 - y^-1 = 3/2 - 4/3 = (9 - 8)/6 = 1/6 Then, the rational number between (x - y)^-1 and x-1 - y^-1 = (-12 + 1/6)/2 = (1 - 72)/12 = -71/12 A rational number is a number that is expressed as the ratio of two integers, where the denominator should not be equal to zero. For example : 2, 6/5, -9/12, etc. Rational number between two numbers a and b = (a + b)/2.

If \(x = \frac{2}{3}\) and \(y = \frac{3}{4}\), then a rational number between (x - y)-1 and (x-1 - y-1) is1. \(-\frac{71}{12}\)2. \(\frac{1}{6}\)3. \(\frac{2}{3}\)4. \(-\frac{71}{2}\)

Answer» Correct Answer - Option 1 : \(-\frac{71}{12}\)

Calculation :

x = 2/3 and y = 3/4

x - y = 2/3 - 3/4 = (8 - 9)/12 = -1/12

∴ (x - y)^-1 = -12

x^-1 = 3/2 and y^-1 = 4/3

x^-1 - y^-1 = 3/2 - 4/3 = (9 - 8)/6 = 1/6

Then, the rational number between (x - y)^-1 and x-1 - y^-1 = (-12 + 1/6)/2 = (1 - 72)/12 = -71/12

A rational number is a number that is expressed as the ratio of two integers, where the denominator should not be equal to zero. For example : 2, 6/5, -9/12, etc.

Rational number between two numbers a and b = (a + b)/2.

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