Question

the denominator of a rational number is 2 less than its numerator is the numerator is decreased by 5 the denominator is increased by 1 the new number becomes 2 upon 3 find the original number​

Answer 1

Original number = 13 / 11

Step-by-step explanation:

Assume:

Numerator of a rational number = x

So,

Denominator of a rational number = x - 2

Rational number =
`(x)/(x-2)`

Numerator decreased by 5 the denominator is increased by 1

New Rational number = 2/3

So,

`(x-5)/(x-2+1)=(2)/(3)\\\\(x-5)/(x-1) = (2)/(3)\\\\x=13`

So,

Numerator of a rational number = 13

Denominator of a rational number = 13 - 2

Denominator of a rational number = 11

Original number = 13 / 11