Answer
$\dfrac{3\sqrt{2}}{4x}$
Work Step by Step
Using the properties of radicals, the expression $
\sqrt{\dfrac{8}{x^2}}-\sqrt{\dfrac{50}{16x^2}}
$ simplifies to
\begin{array}{l}
\sqrt{\dfrac{4}{x^2}\cdot2}-\sqrt{\dfrac{25}{16x^2}\cdot2}
\\\\=
\dfrac{2\sqrt{2}}{x}-\dfrac{5\sqrt{2}}{4x}
\\\\=
\dfrac{4(2\sqrt{2})-1(5\sqrt{2})}{4x}
\\\\=
\dfrac{8\sqrt{2}-5\sqrt{2}}{4x}
\\\\=
\dfrac{3\sqrt{2}}{4x}
.\end{array}
