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# The Denominator of a Fraction is One More than Twice the Numerator. If the Sum of the Fraction and Its Reciprocal is 2.9; Find the Fraction - Mathematics

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#### Question

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

#### Solution

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

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

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