Question

The denominator of a positive fraction is one more than twice the numerator. If the sum of the fraction and its reciprocal is 2.9; find the fraction.

Answer 1

Let the required fraction be `x/(2x + 1)`

From the given information,

`x/(2x + 1) + (2x + 1)/x = 2.9`

`(x^2 + 4x^2 + 1 + 4x)/(x(2x + 1)) = 29/10`

`(5x^2 + 1 + 4x)/(2x^2 + x) = 29/10`

`50x^2 + 10 + 40x = 58x^2 + 29x`

`8x^2 - 11x - 10 = 0`

`x = (11 +- sqrt(121 + 320))/16`

`x = (11+-sqrt441)/16`

`x = (11 +- 21)/16`

`x = 2, -5/8`

Thus, the required fraction is `2/5`