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Let the fractions be x and y:-

If: 2x+3y = 31

Then: 2/31x+3/31y = 1 by dividing all terms by 31

So: 2/31*31/4 + 3/31*31/6 = 1 because 1/2+1/2 = 1

Therefore: x = 31/4 and y = 31/6

Check: 2*31/4 + 3*31/6 = 31

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