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Answer :
Given that,\(\frac{n}2-\frac{3n}4+\frac{5n}6=21\)
LCM of denominators 2,4 and 6=12
So, \(\frac{n}2×12-\frac{3n}4×12+\frac{5n}6×12=21×12\quad \)[Multiplying both the sides by 12]
\(\Rightarrow 6n-9n +10n = 252\)
\(\Rightarrow 7n = 252\)
\(\Rightarrow n = 252÷7\quad \)[Dividing both the sides by 7]
\(\Rightarrow n = 36\)