Question

the denominator of a fraction is one more than twice its numerator. if 2 is added to denominator the fraction becomes 5/8. find the original number

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

Answer 2

Step-by-step explanation:

$\frac{x}{2x + 1 +2 } = \frac{5}{8} \\ 8x = 10x + 5 + 10 \\ 8x - 10x = 15 \\ - 2x = 15 \\ x = \frac { - 15}{2}$