Question

The denominator of a fraction is one more than twice the numerator if the sum of the fraction and it's reciprocal is 58 by 21 find the fraction

Answer 1

$fraction = \frac{3}{7}$
thank you

Answer 2

$\Large{\textbf{\underline{\underline{According\;to\;the\;Question}}}}$

Assumption,

Numerator be p

Also,

Denominator be 2p + 1

So,

Fraction = p/(2p + 1)

Now,

Reciprocal = (2p + 1)/p

Situation,

p/(2p + 1) + (2p + 1)/p = 58/21

21{p² + (2p + 1)²} = 58p(2p + 1)

21{5p² + 4p + 1} = 116p² + 58p

11p² - 26p - 21 = 0

Now,

Splitting the middle term,

11p² - 33p + 7p - 21 = 0

11p(p - 3) + 7(p - 3) = 0

(p - 3)(11p + 7) = 0

p - 3 = 0 or 11p + 7 = 0

p = 3, -7/11 (Negative value is not acceptable)

p = 3

Numerator = p = 3

Denominator

= 2p + 1

= 2(3) + 1

= 6 + 1

= 7

Fraction = 3/7