Question 736937
 The sum of the reciprocal of a number and the reciprocal of 3 less than the number is 6 times the reciprocal of the original number.
 Find the original number
:
let n = original number
:
{{{1/n}}} + {{{1/((n-3))}}} = {{{6/n}}}
multiply by n(n-3), resulting in
(n-3) + n = 6(n-3)
n - 3 + n = 6n - 18
2n - 6n = -18 + 3
-4n = -15
n = -15/-4
n = +3.75 is the original number
:
:
Expected an integer here, see if this checks out:
{{{1/3.75}}} + {{{1/.75}}} = {{{6/3.75}}}
.267 + 1.333 = 1.6, it does!