The sum of two fractions is three times their difference. six times the smaller fraction exceeds the larger fraction by 3/2. find the fractions

Let a and b represent the fractions.

... a + b = 3 (b - a)

... 6a - b = 3/2

Rewriting the first equation, we have

... 4a - 2b = 0

or

... 2a - b = 0

Subtracting this from the second equation gives

... 4a = 3/2

... a = 3/8

... b = 2a = 3/4

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