If $m = -\dfrac{7}{9}$ and $n = \dfrac{5}{6}$, verify that:

m - n ≠ n - m

To prove:

m - n ≠ n - m

LHS:

$m - n\\[1em] -\dfrac{7}{9} - \dfrac{5}{6}$

LCM of 9 and 6 is 2 x 3 x 3 = 18

$-\dfrac{7 \times 2}{9 \times 2} - \dfrac{5 \times 3}{6 \times 3}\\[1em] = -\dfrac{14}{18} - \dfrac{15}{18}\\[1em] = \dfrac{-14 - 15}{18}\\[1em] = \dfrac{-29}{18}\\[1em] = -1\dfrac{11}{18}$

RHS:

$n - m\\[1em] \dfrac{5}{6} - \Big(-\dfrac{7}{9}\Big)\\[1em] = \dfrac{5}{6} + \dfrac{7}{9}$

LCM of 6 and 9 is 2 x 3 x 3 = 18

$= \dfrac{5 \times 3}{6 \times 3} + \dfrac{7 \times 2}{9 \times2}\\[1em] = \dfrac{15}{18} + \dfrac{14}{18}\\[1em] = \dfrac{15 + 14}{18}\\[1em] = \dfrac{29}{18}\\[1em] = 1\dfrac{11}{18}$

Hence, LHS ≠ RHS

m - n ≠ n - m