7. The denominator of a rational number is greater than its numerator

1.	7. The denominator of a rational number is greater than its numerator by 8. If thenumerator is increased by 17 and the denominator is decreased by 1, the number3obtained is2Find the rational number.
Answer» Let the numerator of the rational NUMBER be X. So as PER the GIVEN CONDITION, the denominator will be x + 8. $The \: rational \: number \: will \: \\ be \frac{x}{x + 8}$ According to the given condition, $\frac{(x + 17) }{x + 8 - 1} = \frac{3}{2}$ $\frac{x + 17}{x + 7} = \frac{3}{2}$ 3(x + 7) = 2(x + 17) 3x + 21 = 2x + 34 3x – 2x + 21 – 34 = 0 x – 13 = 0 x = 13 The rational number will be $\frac{x}{x + 8}$ $\frac{13}{13 + 8}$ Rational number = 13/21