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

Anurag Mishra Professor Asked on 23rd February 2016 in Maths.
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1 Answer(s)

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.

Anurag Mishra Professor Answered on 25th February 2016.
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