#(1/(x+1)) - 1/x = 1/2#
#(x - x - 1) / (x * (x+1)) = 1/2, " taking L C M for L H S"#
#-1 * 2 = x * (x + 1), " cross multiplying"#
#x^2 + x = - 2#
#x^2 + x + 2 = 0#
#"Applying the above formula with " #a = 1, b = 1, c = 2#
" for finding the roots"#,
#x_+ = (-1 + (sqrt(1-8))) / 2 = (-1 + isqrt7)/2#
#x_- = (-1 - (sqrt(1-8))) / 2 = (-1 - isqrt7)/2#