Denominator of a fraction is one more than twice the numerator if the sum of fraction and reciprocal = 58/21 ?

Question

find the fraction

Answer 1

Let N be the numerator

Let D be the denominator

Equation 1:

N/D + D/N = 58/21

Equation 2:

D = 2N + 1

N²/ND + D²/ND = 58/21

(N² + D²)/ND = 58/21

Cross multiply:

58ND = 21(N² + D²)

Substitute:

58N(2N + 1) = 21(N² + (2N+1)²)

116N² + 58N = 21(N² + 4N² + 4N + 1)

116N² + 58N = 21(5N² + 4N + 1)

116N² + 58N = 105N² + 84N + 21

9N² - 26N - 21 = 0

Quadratic formula:

N = 3.5468

or

N = -0.65788

Hmm... something doesn't seem right with the details of the question

Answer 2

x/y +y/x=58/21

y=2x+1

solve these two equations together.