The denominator of a rational number is greater than its numerator by 8. If the numerator is increased by 17 and the denominator decreased by 1, the number obtained is 3/2. Find the rational number.

numerator = x

denominator = x+8

so, numerator is increased by 17 and denominator decreased by 1.

x+17 / x+8-1 = 3/2

x+17 / x+7 = 3/2

(now, cross multiply)

3 (x+7) = 2 (x+17)

3x + (3*7) = 2x + (2*17)

3x + 21 = 2x + 34

3x - 2x = 34 - 21

x = 13

therefore, the rational number is 13/20