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

Answer:

$\frac{3}{5}$

Step-by-step 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 $\frac{1}{2}$

• $\implies \frac{x-2-1}{x-1}=\frac{1}{2}$

• $\implies \frac{x-3}{x-1}=\frac{1}{2}$

• $\implies 2(x-3)=x -1$

• $\implies 2x-6=x -1$

• $\implies 2x-x=6-1$

• $\implies x=5$

• $\implies x-2=-5-2= 3$

• $Required \: rational\: number = \frac{3}{5}$