## Elementary Algebra

$-1$
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, $\dfrac{2-3[(4-5)^2+1]}{(3-1)^2} ,$ simplifies to \begin{array}{l}\require{cancel} \dfrac{2-3[(-1)^2+1]}{(2)^2} \\\\= \dfrac{2-3[(-1)(-1)+1]}{(2)(2)} \\\\= \dfrac{2-3[1+1]}{4} \\\\= \dfrac{2-3[2]}{4} \\\\= \dfrac{2-6}{4} \\\\= \dfrac{-4}{4} \\\\= -1 .\end{array}