Question

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

Answer 1

Let Numerator=x
Question Saying Denominator is 8 more than Numerator.
Denominator=x+8
$fraction = \frac{x}{x + 8}$
If 17 is added to Numerator
Numerator=x+17

If 1 is Decreased by Denominator
=x+8-1=x+7

It become=3/2
MEANS

$\frac{x + 17}{x + 7} = \frac{3}{2} \\ 2(x + 17) = 3(x + 7) \\ 2x + 34 = 3x + 21 \\ 2x - 3x = 21 - 34 \\ \cancel - x = \cancel- 13 \\ x = 13$
Numerator=x=13
Denominator=x+8=13+8=21

$\boxed{\mathbf{Original \:Rational\: number=\frac{13}{21}}}$

Answer 2

Solution:

Let the numerator be x then denominator will be $(x+8)$

According to the question,

$\frac{(x+17)}{(x+8-1)} = \frac{3}{2} \\\implies \frac{(8+16)}{(8+7)} = \frac{3}{2} \\\implies 2(x+17)=3(x+7)\\\implies 2x+34=3x+21\\\implies 34-21=3x-2x\\\implies 13=x$

∴ The rational number is $:\implies$  $\boxed{\frac{x}{x+8}=\frac{13}{21}}$

Therefore, the rational number is $\frac{13}{21}$