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Question

(A) Let the fraction be $x$.According to the problem,the fraction is greater than its reciprocal by $\frac{9}{20}$,so:$x - \frac{1}{x} = \frac{9}{20}$

Vedclass · Accepted Answer

$\frac{5}{4}$

Vedclass · Answer

(A) Let the fraction be $x$.According to the problem,the fraction is greater than its reciprocal by $\frac{9}{20}$,so:$x - \frac{1}{x} = \frac{9}{20}$Multiply the entire equation by $20x$ to clear the denominators:$20x^2 - 20 = 9x$Rearrange into a standard quadratic equation form:$20x^2 - 9x - 20 = 0$Factor the quadratic equation:$20x^2 - 16x + 25x - 20 = 0$$4x(5x - 4) + 5(5x - 4) = 0$$(4x + 5)(5x - 4) = 0$This gives two possible values for $x$:$x = -\frac{5}{4}$ or $x = \frac{4}{5}$ is incorrect based on the positive difference. Let's re-evaluate:If $x = \frac{5}{4}$,then the reciprocal is $\frac{4}{5}$.Difference: $\frac{5}{4} - \frac{4}{5} = \frac{25 - 16}{20} = \frac{9}{20}$.Thus,the fraction is $\frac{5}{4}$.

$A$ fraction is greater than its reciprocal by $\frac{9}{20}$. What is the fraction?

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