Chapter R - Section R.3 - Exponents, Roots, and Order of Operations - R.3 Exercises - Page 30: 77

$-7$

Using order of operations, the given expression, $ \dfrac{5-3\left(\dfrac{-5-9}{-7}\right)-6}{-9-11+3\cdot7} ,$ simplifies to \begin{array}{l}\require{cancel} \dfrac{5-3\left(\dfrac{-14}{-7}\right)-6}{-9-11+21} \\\\= \dfrac{5-3\left(2\right)-6}{-20+21} \\\\= \dfrac{5-6-6}{1} \\\\= \dfrac{-1-6}{1} \\\\= \dfrac{-7}{1} \\\\= -7 .\end{array}