Answer
$-\dfrac{7}{9}$
Work Step by Step
Recall, in order to solve problems involving order of operations, we use the PEMDAS rule.
First Priority: P - parentheses and other grouping symbols (including fraction bars)
Second Priority: E - exponents
Third Priority: M/D - Multiplication or division, whichever comes first from the left to the right
Fourth Priority: A/S - Addition or subtraction, whichever comes first from the left to the right
We follow order of operations to obtain that the expression, $
\dfrac{-3-2[(3-5)^2-2]}{(-2-1)^2}
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{-3-2[(-2)^2-2]}{(-3)^2}
\\\\=
\dfrac{-3-2[(-2)(-2)-2]}{(-3)(-3)}
\\\\=
\dfrac{-3-2[4-2]}{9}
\\\\=
\dfrac{-3-2[2]}{9}
\\\\=
\dfrac{-3-4}{9}
\\\\=
\dfrac{-7}{9}
\\\\=
-\dfrac{7}{9}
.\end{array}
