Evaluate:

$\dfrac{4}{7} + 0 + \dfrac{-8}{9} + \dfrac{-13}{7} + \dfrac{17}{9}$

$\dfrac{4}{7} + \dfrac{0}{1} + \dfrac{-8}{9} + \dfrac{-13}{7} + \dfrac{17}{9}$

LCM of 7 ,1 and 9 is 3 x 3 x 7 = 63

$\dfrac{4 \times 9}{7 \times 9} + \dfrac{0 \times 63}{1 \times 63} + \dfrac{-8 \times 7}{9 \times 7} + \dfrac{-13 \times 9}{7 \times 9} + \dfrac{17 \times 7}{9 \times 7} \\[1em] = \dfrac{36}{63} + \dfrac{0}{63} + \dfrac{-56}{63} + \dfrac{-117}{63} + \dfrac{119}{63} \\[1em] = \dfrac{36 + 0 + (-56) + (-117) + 119}{63} \\[1em] = \dfrac{-18}{63} \\[1em]$

∴ $\dfrac{4}{7} + 0 + \dfrac{-8}{9} + \dfrac{-13}{7} + \dfrac{17}{9} = \dfrac{-18}{63}$