let

x = the numerator

y = the denominator, y <> 0

x/y = the fraction we want to find

The numerator of a fraction is 1 less than the denominator:

x = y - 1

If the numerator and the denominator are both increased by 4, the new fraction will be 1/8 more than the original fraction:

(x + 4)/(y + 4) = (1/8) + x/y

plug x = y - 1 into the last equation:

(y - 1 + 4)/(y + 4) = (1/8) + (y - 1)/y

by solving we find:

y1 = 4

y2 = - 8

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Solution 1: for y = 4 we find x = 4 - 1 = 3 and the fraction is 3/4

Solution 2: for y = - 8 we find x = - 8 - 1 = -9 and the fraction is -9/-8