The ran of the reciprocal of a number and the reciprocal of

The ran of the reciprocal of a number and the reciprocal of 2 less than the number is 8 tines the reciprocal of the original number. Find the original number.

Solution

let the original number be x

Reciprocal of the number = 1/x

Reciprocal of 2 less than number = 1/(x -2)

8 times reciprocal of number = 8/x

Given sum of Reciprocal of the number and Reciprocal of 2 less than number = 8 times reciprocal of number

==> 1/x + 1/(x -2) = 8/x

==> [(x -2) + x]/[x(x -2)] = 8/x

==> (2x -2)/(x -2) = 8

==> 2x -2 = 8(x - 2)

==> 2x -2 = 8x - 16

==> 8x - 2x = -2 + 16

==> 6x = 14

==> x = 14/6

==> x = 7/3

Hence the original number is 7/3