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.
According to the given condition: when 1 is subtracted from numerator and denominator both, the resulting new rational number in its simplest form is [tex]\frac{1}{2}[/tex]
[tex]\implies \frac{x-2-1}{x-1}=\frac{1}{2}[/tex]
[tex]\implies \frac{x-3}{x-1}=\frac{1}{2}[/tex]
[tex]\implies 2(x-3)=x -1[/tex]
[tex]\implies 2x-6=x -1[/tex]
[tex]\implies 2x-x=6-1[/tex]
[tex]\implies x=5[/tex]
[tex]\implies x-2=-5-2= 3[/tex]
[tex] Required \: rational\: number = \frac{3}{5}[/tex]
