Answer
$\dfrac{1}{11}$
Work Step by Step
Using order of operations, the expression $
\dfrac{(3-5)^2+(-1)^3}{1+2(3-(-1))^2}
$ simplifies to
\begin{array}{l}
\dfrac{(-2)^2-1}{1+2(3+1)^2}
\\\\=
\dfrac{4-1}{1+2(4)^2}
\\\\=
\dfrac{3}{1+2(16)}
\\\\=
\dfrac{3}{1+32}
\\\\=
\dfrac{3}{33}
\\\\=
\dfrac{1}{11}
.\end{array}
