Answer
$-x^5+2x^4-2x^2-x$
Work Step by Step
By combining like terms, the given expression, $
\left(x^4-2x^2-\dfrac{1}{2}x \right)-\left( x^5-x^4+\dfrac{1}{2}x \right)
$, simplifies to
\begin{array}{l}\require{cancel}
x^4-2x^2-\dfrac{1}{2}x-x^5+x^4-\dfrac{1}{2}x
\\\\=
-x^5+(x^4+x^4)-2x^2+\left( -\dfrac{1}{2}x-\dfrac{1}{2}x \right)
\\\\=
-x^5+2x^4-2x^2-x
.\end{array}
