# If x = 2/3 and y = 3/4, then a rational number between

If x = 2/3 and y = 3/4, then a rational number between (x – y)^{-1} and (x^{-1} – y^{-1}) is

(a) 2/3

(b) -71/2

(c) -71/12

(d) 1/6

**Answer: (c) -71/12**

**Solution:-**

x = 2/3 and y = 3/4

Then, x – y = 2/3 – 3/4

= (8 – 9)/12

= -1/12

(x – y)^-1 = -12

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

Then, 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) = (1/6 -12)/2

= (1 – 72)/12

= -71/12

Hence, the correct answer is option (c) -71/12.