Question

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The denominator of a rational number is greater than its numerator by 8. If the numerator is increased by 7 and the denominator is increased by 1 the number obtained is 2/3 . Find the rational number? ​

Answer 1

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{Rational\:number\:is\:=\:\frac{-3}{5}}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\sf{Let\:numerator\:be\:x}$

$\sf{so,\:denominator\:will\:be\:x\:+\:8}$

$\implies{x+\frac{7}{x}+8+1=\frac{2}{3}}$

$\implies{x+\frac{7}{x}+9=\frac{2}{3}}$

$\implies{3(x+7)=2(x+9)}$

$\implies{3x+21=2x+18}$

$\implies{3x-2x=18-21}$

$\implies{x= - 3}$

$\implies$$\frac{x}{x+8}=\frac{-3}{5}$

$\therefore$Rational number is $\frac{-3}{5}$

Answer 2

Answer:

-3/5

Step-by-step explanation:

let the numerator be x..

then denominator=x+8...

according to the question,

x+7/x+8+1= 2/3

x+7/x+9= 2/3

3(x+7)=2(x+9)

3x+21= 2x+18

3x-2x= 18-21

x= -3

numerator= -3

denominator= 5

rational no. = -3/5