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 is 3/2 find the rational number​

Answer 1

$\huge\underline{\underline{\bf\bigstar ANSWER \bigstar }}$

Let ,

➯  Numerator of the rational number = x

➯  Denominator of the rational number = x + 8

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According to the question ,

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

     $\hookrightarrow \sf \dfrac{x+17}{x+7}=\dfrac{3}{2}\\\\\hookrightarrow 2(x+17)=3(x+7)\\\\\hookrightarrow 2x+34 = 3x + 21\\\\\hookrightarrow 3x-2x = 34-21\\\\\hookrightarrow \underline{\underline{\bf x =13}}$

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➥ Numerator of the rational number = 13

➥ Denominator of the rational number = 21

   

   $\bf\Longrightarrow Rational \ number = \dfrac{13}{21}$

HOPE IT HELPS U ............... :)

Answer 2

Answer:

Numerator of the rational number = x = 13

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

Rational number = 13/21

Step-by-step explanation:

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 x/x + 8.

According to the given cndition,

x + 17/x + 8 – 1 = 3/2

=x + 17/x + 7 = 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 = 13/21