consider the balanced reaction to be
a XeF6 + b H2O ---> c XeO3 + d HF
first balance the Xe atoms :
number of Xe atoms on left side = number of Xe atoms on right side
a = c
similarly , balance the F atoms : 6a = d
similarly , balance the H atoms : 2b = d
balance the O atoms : b = 3c
now combine all the relations to get
a = c = b/3 = d/6
consider the ratio
a : b : c : d = a : 3a : a : 6a
a : b : c : d = 1 : 3 : 1 : 6
so
a = 1
b = 3
c = 1
d = 6
plug in the values to get the balanced reaction
XeF6 + 3 H2O ---> XeO3 + 6 HF
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