Question

the denominator of a rational number is greater than its numerator by 8 . if the numerator is increased by 17 and the denominator is decreased by 1 , the number obtained is 3/2. find the raitional number​

Answer 1

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,

$x + \frac{17}{x} + 8 - 1 = \frac{3}{2}$

$= x + \frac{17}{x} + 7 = \frac{3}{2}$

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

$= 2x + 34 = 3x + 21$

$= 34 - 21 = 3x - 2x$

$= x = 13$

Numerator of the rational number = x = 13

Denominator of the rational number = x + 8 = 13 + 8 = 21

Rational number

$= \frac{13}{21}$