Question

the numerator of a rational number is less than its denominator by 2.If 1 is added to both the numerator and the denominator the rational number is obtained is 2/3,what is the rational number?

Answer 1

Let the fraction (rational number) be x-2/x
Then,x-2+1/x+1=2/3
x-1/x+1=2/3
3(x-1)=2(x+1)
3x-3=2x+2
3x-2x=2+3
x=5
therefore the fraction is 3/5

Answer 2

Let the denominator be x then the numerator will be x-2
Now, ATQ
$\frac{x - 2 + 1}{x + 1} = \frac{2}{3} \\ \frac{x - 1}{x + 1} = \frac{2}{3} \\ 3(x - 1) = 2(x + 1) \\ 3x - 3 = 2x + 2 \\ 3x - 2x = 3 + 2 \\ x = 5$
Now x = 5
Then numerator = 5-2 =3
Denominator = 5