Question

The denominator of a fraction is 1 more than double the numerator. On adding 2 to the numerator and subtracting 3 from the denominator, we obtain 1 Find the original f
fraction. ​

Answer 1

Answer:

Let the numerator of the fraction be x.

Then Denominator=2x+1

Fraction =

2x+1

x

​

Reciprocal of the fraction =

x

2x+1

​

It is given that the sum fo the fraction and its reciprocal is 2

21

16

​

∴

2x+1

x

​

+

x

2x+1

​

=2

21

16

​

⇒

x(2x+1)

x

2

+(2x+1)

2

​

=

21

58

​

⇒

2x

2

+x

5x

2

+4x+1

​

=

21

58

​

⇒21(5x

2

+4x+1)=58(2x

2

+x)⇒105x

2

+84x+21=116x

2

+58x

⇒11x

2

−26x−21=0⇒11x

2

−33x+7x−21=0⇒11x(x−3)+7(x−3)=0

⇒(11x+7)(x−3)=0⇒x=3,−

11

7

​

∵ x can not be a negative

⇒x=3

Hence the fraction =

2x+1

x

​

=

7

3

​

Step-by-step explanation:

Answer 2

Answer:

Let numerator be x

let denominator be 2x+1

Step-by-step explanation:

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

x+2/2x-2=1

x+2=2x-2

2+2=2x-x

x=4

numerator=4

denominator=2x+1=9

Hope this helps:)