Question

the denominator of the fraction is grater than the denominator by 8.if the numerator is increased by 17 and denominator is decreased by 1 the number obtained is 3/2find the fraction
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Answer 1

Step-by-step explanation:

Let the numerator of the rational number be x. Therefore, its denominator will be x + 8. The rational number will be x/x + 8. According to the question, 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 ⇒13 = x Numerator of the rational number = x = 13 Denominator of the rational number = x + 8 = 13 + 8 = 21 Rational number = 13/21

Answer 2

Let the numerator be x

So, denominator be x + 8

We know

$\red{ \rm Fraction = \dfrac{Numerator}{Denominator}}$

So,

$\rm \dfrac{x}{x+8}$

So, we get the fraction

$\bf \dfrac{x}{x+8}$

Now according to question

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

→ $\sf 2(x+1) = 3(x+7)$

→ $\sf \dfrac{x+1}{x+7} = \dfrac{3}{2}$

→ $\sf 2x+2 = 3x+21$

→ $\sf -x = 19$

So, we got the value of x which is -19

So, simply subsituting in our fraction

$\rm \dfrac{x}{x+8}$

$\implies \sf \dfrac{-19}{-19+8}$

$\implies \sf \dfrac{-19}{-11}$

So, finally we got the fraction which is :-

$\green{\underbrace{\boxed{\overbrace{\dfrac{-19}{-11}}}}}$