question_answer

If numerator is 2 less than denominator of a rational number and when 1 is subtracted from numerator and denominator both, the rational number in its simplest from is\[\frac{1}{2}~\] . What is the rational number?

Answer:

Let the denominator be x, the numerator \[=x-2\]

\[\therefore \] Fraction \[=\frac{x-2}{x}\]

According to given condition,

\[\frac{x-2-1}{x-1}=\frac{1}{2}\]

\[\frac{x-3}{x-1}=\frac{1}{2}\]

\[2x-6=x-1\]                                                                                                                                                    \[2x-x=6-1\]

x = 5

\[\therefore \] Rational number \[=\frac{x-2}{x}=\frac{5-2}{5}=\frac{3}{5}\]