Answer
$8x^5+\dfrac{3}{10}x+\dfrac{2}{3}$
Work Step by Step
By combining like terms, the given expression, $
8x^5-\dfrac{1}{3}+\dfrac{4}{5}x+1-\dfrac{1}{2}x
,$ simplifies to
\begin{array}{l}\require{cancel}
8x^5+\left( \dfrac{4}{5}x-\dfrac{1}{2}x \right)+\left(-\dfrac{1}{3}+1 \right)
\\\\=
8x^5+\left( \dfrac{8}{10}x-\dfrac{5}{10}x \right)+\left(-\dfrac{1}{3}+\dfrac{3}{3} \right)
\\\\=
8x^5+\dfrac{3}{10}x+\dfrac{2}{3}
.\end{array}
