let 'x' and 'y' be the fractions and let x>y

the sum of two fractions is three times their difference

x + y = 3(x - y)

6 times the smaller fractions exceeds the larger fraction by 1 half

6y = x + 1/2

by solving the system of equations

x + y = 3(x - y)

6y = x + 1/2

we find

x = 1/4

y = 1/8

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the fractions are 1/4 and 1/8.