# The denominator of a fraction is one more than twice the numerator. If the sum of the fraction and its reciprocal is , find the fraction.

Let the numerator be ‘X’, so the denominator will be ‘(2X+1)’.

the fraction is

On simplifying further,

21(5X2 + 4X + 1) = 58 (2X2 + X)

105X2 + 84X + 21 = 116X2 + 58X

11X2 – 26X – 21 = 0–––––– (i)

On applying Sreedhracharya formula

X= or 3

X = 3 (Only positive values)

Numerator is = 3 & denominator is (2X+1) = 7

The fraction is .

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