Chapter 10 - Exponents and Radicals - 10.5 Expressions Containing Several Radical Terms - 10.5 Exercise Set - Page 661: 67

$-1$

Factoring the $-1$ from the numerator, the given expression, $ \dfrac{\sqrt{7}-\sqrt{3}}{\sqrt{3}-\sqrt{7}} ,$ simplifies to \begin{array}{l}\require{cancel} \dfrac{-(-\sqrt{7}+\sqrt{3})}{\sqrt{3}-\sqrt{7}} \\\\= \dfrac{-(\sqrt{3}-\sqrt{7})}{\sqrt{3}-\sqrt{7}} \\\\= \dfrac{-(\cancel{\sqrt{3}-\sqrt{7}})}{\cancel{\sqrt{3}-\sqrt{7}}} \\\\= -1 .\end{array}