#### Answer

$\dfrac{8}{1+\sqrt{10}}=-\dfrac{8(1-\sqrt{10})}{9}$

#### Work Step by Step

$\dfrac{8}{1+\sqrt{10}}$
Multiply the numerator and the denominator of this expression by the conjugate of the denominator and simplify if possible:
$\dfrac{8}{1+\sqrt{10}}=\dfrac{8}{1+\sqrt{10}}\cdot\dfrac{1-\sqrt{10}}{1-\sqrt{10}}=\dfrac{8(1-\sqrt{10})}{1^{2}-(\sqrt{10})^{2}}=...$
$...=\dfrac{8(1-\sqrt{10})}{1-10}=\dfrac{8(1-\sqrt{10})}{-9}=-\dfrac{8(1-\sqrt{10})}{9}$