Chapter 6 - Rational Expressions and Equations - 6.3 Addition, Subtraction, and Least Common Denominators - 6.3 Exercise Set - Page 393: 32

$0$

Subtracting the numerators and copying the denominator, the given expression, $ \dfrac{3a^2+7}{a^2-2a-8}-\dfrac{7+3a^2}{a^2-2a-8} ,$ simplifies to \begin{array}{l}\require{cancel} \dfrac{3a^2+7-(7+3a^2)}{a^2-2a-8} \\\\= \dfrac{3a^2+7-7-3a^2}{a^2-2a-8} \\\\= \dfrac{0}{a^2-2a-8} \\\\= 0 .\end{array}