Question

The numerator of a rational number is 2 less than the denominator. If the denominator is increased by 6 and the numerator by 3 , we got the rational number 1/3. Find the rational number​

Answer 1

Answer:

Let the numerator of the rational number be x.

Let the numerator of the rational number be x. Then, the denominator of the rational number =x+3

Let the numerator of the rational number be x. Then, the denominator of the rational number =x+3According to the given condition,

Let the numerator of the rational number be x. Then, the denominator of the rational number =x+3According to the given condition,New numerator =3x and new denominator =(x+3)+20=x+23

Let the numerator of the rational number be x. Then, the denominator of the rational number =x+3According to the given condition,New numerator =3x and new denominator =(x+3)+20=x+23Given,

Let the numerator of the rational number be x. Then, the denominator of the rational number =x+3According to the given condition,New numerator =3x and new denominator =(x+3)+20=x+23Given, x+23

Let the numerator of the rational number be x. Then, the denominator of the rational number =x+3According to the given condition,New numerator =3x and new denominator =(x+3)+20=x+23Given, x+233x

Let the numerator of the rational number be x. Then, the denominator of the rational number =x+3According to the given condition,New numerator =3x and new denominator =(x+3)+20=x+23Given, x+233x

Let the numerator of the rational number be x. Then, the denominator of the rational number =x+3According to the given condition,New numerator =3x and new denominator =(x+3)+20=x+23Given, x+233x =

1/8

By cross multiplying, we get

By cross multiplying, we get8(3x)=x+23

By cross multiplying, we get8(3x)=x+23⇒24x=x+23

By cross multiplying, we get8(3x)=x+23⇒24x=x+23⇒23x=23 ....[On Transposing]

By cross multiplying, we get8(3x)=x+23⇒24x=x+23⇒23x=23 ....[On Transposing]or x=1

By cross multiplying, we get8(3x)=x+23⇒24x=x+23⇒23x=23 ....[On Transposing]or x=1Therefore, numerator of the rational number =1 and denominator =1+3=4.

By cross multiplying, we get8(3x)=x+23⇒24x=x+23⇒23x=23 ....[On Transposing]or x=1Therefore, numerator of the rational number =1 and denominator =1+3=4.Hence, the original rational number is

1/4