Answer
$\frac{-9+\sqrt7}{74}$
Work Step by Step
$\frac{-1}{9+\sqrt7}=\frac{-1(9-\sqrt7)}{(9+\sqrt7)(9-\sqrt7)}=\frac{-9+\sqrt7}{9^2-(\sqrt7)^2}=\frac{-9+\sqrt7}{81-7}=\frac{-9+\sqrt7}{74}$
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