Evaluate:

$\dfrac{3}{7} + \dfrac{-4}{9} + \dfrac{-11}{7} + \dfrac{7}{9}$

LCM of 7 and 9 is 3 x 3 x 7 = 63

$\dfrac{3 \times 9}{7 \times 9} + \dfrac{-4 \times 7}{9 \times 7} + \dfrac{-11 \times 9}{7 \times 9} + \dfrac{7 \times 7}{9 \times 7} \\[1em] = \dfrac{27}{63} + \dfrac{-28}{63} + \dfrac{-99}{63} + \dfrac{49}{63} \\[1em] = \dfrac{27 + (-28) + (-99) + 49}{63} \\[1em] = \dfrac{-51}{63} \\[1em]$

∴ $\dfrac{3}{7} + \dfrac{-4}{9} + \dfrac{-11}{7} + \dfrac{7}{9} = \dfrac{-51}{63}$