The difference between a positive proper fraction and its reciprocal is 9/20. The fraction is:
$ \dfrac{3}{5} $
$ \dfrac{3}{10} $
$ \dfrac{4}{5} $
$ \dfrac{4}{3} $
Explanation:
$\Rightarrow$ 20 - 20$ x $2 = 9$ x $
$\Rightarrow$ 20$ x $2 + 9$ x $ - 20 = 0
$\Rightarrow$ 20$ x $2 + 25$ x $ - 16$ x $ - 20 = 0
$\Rightarrow$ 5 x $\left(4x+ 5\right)$ - 4$\left(4x + 5\right)$ = 0
$\Rightarrow$ $\left(4 x + 5\right)$ x $\left(5 x - 4\right)$ = 0
$x$ =$ \dfrac{4}{5} $