Question

The denominator of a fraction is one more than twice the numerator iif the s
um of fraction and its reciprical is 2 16/21 find fraction

Answer 1

Let the fraction be x/y

According to the question y = 2x + 1

It's already said that ,

the sum of fraction and its reciprical is 2 16/21

So,

$\frac{x}{y} + \frac{y}{x} = 2 \frac{16}{21} = \frac{58}{21} \\ \\ \frac{x}{2x + 1} + \frac{2x + 1}{x} = \frac{58}{21} \\ \\ \frac{ {x}^{2} + {4x}^{2} + 1 + 4x }{x(2x + 1)} = \frac{58}{21} \\ \\ = > {105x}^{2} + 84x + 21 = 116 {x}^{2} + 58x \\ \\ = > (x - 3)(11x + 7) = 0 \\ \\ = > x = 3 \: or \frac{ - 7}{11} \\ x = \frac{ - 7}{11} is \: not \: possible \: beacuse \: x \: cannot \: be \: negative \\ so \: \\ x = 3 \\ \\ since \: fraction \: is\: \frac{x}{2x + 1} \\ \\ = > \frac{3}{2 \times 3 + 1} \\ = > fraction \: is = \frac{3}{7}$

hence , required fraction = 3/7