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Prime factorisation of 18 = 2*3*3

Prime factorisation of 30 = 2*3*5

Then 1/18 = 5*1/5*18 = 5*90 (using the prime factor of 30 that is not in 18)

and 1/30 = 3*1/3*30 = 3*90 (using the extra prime factor of 18 that is not in 30)

So 1/18 + 1/30 = 5/90 + 3/90 = 8/90 = 4/45

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