The sum of the numerator will be (x) ( x - 1) / 2
So we have that
[ (x ) (x - 1) ] / 2
_____________ = 3
x
(x) ( x - 1)
_________ = 3 multiply both sides by 2x
2x
x^2 - x = 6x subtract 6x from both sides
x^2 -7x = 0 factor
x ( x - 7) = 0 set each factor to 0 and solve for x
And x = 0 [reject] or x = 7
Proof
6/7 + 5/7 + 4/7 + 3/7 + 2/7 + 1/7 =
21 / 7 = 3