Question

If numerator is 2 less than the denominator of a rational number and When 1 is subtracted from numerator and denominator both, then the rational number in its simplest form is 1/2. What is the rational number? PLEASE ANSWER IN ONE VARIABLE.

Answer 1

Step-by-step explanation:

Let the denominator be x.

then, numerator=x-2

original fraction=x-2

x

New fraction=x-2-1

x-1

A.T.Q.

New fraction=1/2

=> x-3 = 1

x-1 2

=> 2(x-3) = x-1

=> 2x-6 = x-1

=> 2x-x= -1+6

=> x = 5

So, original fraction= x-2

x

=5-2

5

=3

5

*Hope this will help you. plz give me a thank and mark it as a brainiest answer.

Answer 2

$\mathfrak{\large{\underline{\underline{Answer :-}}}}$

The Rational Number is = $\boxed{\boxed{\bf{\frac{3}{5}}}}$

$\mathfrak{\large{\underline{\underline{Explanation :-}}}}$

Given :

The numerator is 2 less than the denominator

When 1 is subtracted from numerator and denominator, rational number's simplest form = $\tt{\dfrac{1}{2}}$

To find :

The rational number

Solution :

Consider the denominator as x

Numerator = x - 2

★ Equation :

$\boxed{\sf{ \frac{(x - 2) - 1}{x - 1} = \frac{1}{2}}}$

$\sf{\implies} \: {\dfrac{(x - 2) - 1}{x - 1} = \dfrac{1}{2}}$

Cross Multiply them

$\sf{\implies} \: 2(x - 2) - 1 = 1(x - 1)$

$\sf{\implies} \: 2x - 4- 2 = x - 1$

$\sf{\implies} \: 2x - 6 =x - 1$

$\sf{\implies} \: 2x - x = - 1 + 6$

$\sf{\implies} \: x = 5$

★ Value of x - 2

$\sf{\implies} \: 5 - 2$

$\sf{\implies} \: 3$

The Rational number is = $\boxed{\boxed{\bf{\frac{3}{5}}}}$

$\therefore$ The Rational Number is = $\boxed{\boxed{\bf{\frac{3}{5}}}}$

$\rule{300}{1}$

$\mathfrak{\large{\underline{\underline{Verification :-}}}}$

$\sf{\implies} \: {\dfrac{(5- 2) - 1}{5 - 1} = \dfrac{1}{2}}$

$\sf{\implies} \: {\dfrac{3 - 1}{5 - 1} = \dfrac{1}{2}}$

$\sf{\implies} \: {\dfrac{2}{4} = \dfrac{1}{2}}$

Convert it into lowest form :

$\sf{\implies} \: {\dfrac{1}{2} = \dfrac{1}{2}}$

$\therefore$ The Rational Number is = $\boxed{\boxed{\bf{\frac{3}{5}}}}$