Question

The denominator of a fraction is one more than twice its numerator. If the sum of the fraction and its
reciprocal is 2hole16/21
find the fraction.​

Answer 1

Answer:

3/7

Step-by-step explanation:

Let the numerator of the fraction be = x

Then denominator = 2x+1

Fraction = x/2x+1

It is given that the sum of the fraction and it's reciprocal is 2 16/21

therefore. (x/2x+1) + (2x+1/x) = 2 16/21

=> [x^2+(2x+1)^2]/x(2x+1) = 58/21

=> [5x^2+4x+1]/[2x^2+1] = 58/21

=> 21[5x^2+4x+1] = 58[2x^2+1]

=> 105x^2+48x+21 = 106x^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,− 7/11

∵ x can not be a negative

=> x=3

hence the fraction is 3/7