Question 269624
we have
(i) {{{1/x - 1/(x+1) = 1/42}}}
simplify the left side to get
(ii) {{{(1)/(x(x+1)) = 1/42}}}
cross multiply to get
(iii) {{{42 = x^2 + x}}}
set = 0 to get
(iv) {{{x^2 + x -42 = 0}}}
factoring, we get
(v) {{{(x+7)(x-6) = 0}}}
So, x = -7 or x = 6
If x = -7 then x + 1 = -6 and we get -1/7 - (-1/6) = -1/7 + 1/6 = 1/42
If x = 6 then x + 1 = 7 and we get 1/6 - 1/7 = 1/42