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

`(2)/(5)`

Explanation

Let the required fraction be `(a)/((a+3))`. Then,
`(a)/((a+3))+((a+3))/(a)=(29)/(10)implies10[a^(2)+(a+3)^(2)]=29a(a+3)`
`implies9a^(2)+27a-90=0impliesa^(2)+3a-10=0.`