Question

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

Answer 1

Let,

Numerator=x

Denominator=x+8

Given,

Numerator increased by 17 so,

Numerator =x+17

Denominator is decreased by 1 so,

Denominator=x+7

x+17/x+7=3/2

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

2x+34=3x+21

13=x

Therfore,

Rational number=x/x+8

=13/21

Answer 2

let the numerator be x.

=>denominator = x+8

$\: \: \: \: \: \: \: \: \frac{(17 + x)}{(8 + x - 1)} = \frac{3}{2} \\ = > \frac{17 + x}{7 + x} = \frac{3}{2} \\ = > 2(17 + x) = 3(7 + x) \\ = > 34 + 2x = 21 + 3x \\ = > 3x - 2x = 34 - 21 \\ = > x = 13$

Therefore,

numerator = 13

denominator = 13 + 8 = 21