Question

The numerator of a rational number is less than its denominator by 2 . If one is added to both numerator and denominator the rational no obtained is 2/3 find the rational no

Answer 1

Let the denominator be x.

Then the numerator will be x-2.

And the rational number so formed will be x-2/x.

When 1 is added to numerator and denominator becomes x-1 and x+1 respectively.

It is given that,

x-1/x+1=2/3.

By Cross Multiplying:

3(x-1)=2(x+1).
3x-3=2x+2.

Sending 2x from RHS to LHS it becomes -2x and sending -3 from LHS to RHS it becomes 3:

3x-2x=2+3.

x=5.

x-2=3.

The rational number is 3/5 and when 1 is added to numerator and denominator the number becomes 4/6 i.e. 2/3 which is the simplified form of 4/6.

Answer 2

Thanks for asking question

In this type questions we let denominator x

so, numerator is X-2

Then,

Rational number is

$\frac{x - 2}{x}$


Now, if we add numerator and denominator then, x-1,x+2

$\frac{x - 1}{x + 1} = \frac{2}{3}$

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

3x -3 = 2x +2

3x -2x = 2+3

x = 5


Then, x -2 => 5-2 = 3

so, the rational numbers is 3/5 and if we add 1 in numerator and denominator it's become

4/6.2/3


I hope it's help you