let

x = the smaller fraction

y = the larger fraction

the sum of two fraction is three times their difference:

x + y = 3(y - x)

six times the smaller fraction exceeds the larger fraction by 1.5:

6x = y + 1.5

by solving the system of equations:

x + y = 3(y - x)

6x = y + 1.5

we find:

x = 3/8

y = 3/4

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the two fractions are 3/4 and 3/8.