Question

If numerator is 2 less than the denominator of a rational number and when 1 is subtracted from numerator and denominator both, the resulting new rational number in its simplest form is 1/2 . Find the original rational number.​

Answer 1

`(3)/(5)`

Explanation:

• Let the denominator be x
• So, numerator = x - 2
• According to the given condition: when 1 is subtracted from numerator and denominator both, the resulting new rational number in its simplest form is
  `(1)/(2)`

• 
  `\implies (x-2-1)/(x-1)=(1)/(2)`

• 
  `\implies (x-3)/(x-1)=(1)/(2)`

• 
  `\implies 2(x-3)=x -1`

• 
  `\implies 2x-6=x -1`

• 
  `\implies 2x-x=6-1`

• 
  `\implies x=5`

• 
  `\implies x-2=-5-2= 3`

• 
  `Required \: rational\: number = (3)/(5)`