Answer
$-\dfrac{8-8\sqrt{10}}{9}$
Work Step by Step
Rationalizing the denominator of $
\dfrac{8}{1+\sqrt{10}}
$ results to
\begin{array}{l}
\dfrac{8}{1+\sqrt{10}}
\cdot
\dfrac{1-\sqrt{10}}{1-\sqrt{10}}
\\\\=
\dfrac{8-8\sqrt{10}}{(1)^2-(\sqrt{10})^2}
\\\\=
\dfrac{8-8\sqrt{10}}{1-10}
\\\\=
\dfrac{8-8\sqrt{10}}{-9}
\\\\=
-\dfrac{8-8\sqrt{10}}{9}
.\end{array}