A fraction is greater than twice its reciproc | vedclass

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Question

(B) Let the fraction be $x$.According to the problem,the fraction is greater than twice its reciprocal by $\frac{7}{15}$.So,the equation is: $x - 2(\f

Vedclass · Accepted Answer

$\frac{5}{3}$

Vedclass · Answer

(B) Let the fraction be $x$.According to the problem,the fraction is greater than twice its reciprocal by $\frac{7}{15}$.So,the equation is: $x - 2(\frac{1}{x}) = \frac{7}{15}$.Multiply by $15x$ to clear the denominators: $15x^2 - 30 = 7x$.Rearrange into a standard quadratic equation: $15x^2 - 7x - 30 = 0$.Factor the quadratic equation: $15x^2 - 25x + 18x - 30 = 0$.$5x(3x - 5) + 6(3x - 5) = 0$.$(5x + 6)(3x - 5) = 0$.This gives $x = \frac{5}{3}$ or $x = -\frac{6}{5}$.Comparing with the given options,the correct fraction is $\frac{5}{3}$.

$A$ fraction is greater than twice its reciprocal by $\frac{7}{15}$. What is the fraction?

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