The root of polynomial $ p(x) $ is:
$$ \begin{aligned}x &= -\dfrac{ 2 }{ 3 } \end{aligned} $$Step 1:
Get rid of fractions by multipling equation by $ \color{blue}{ 3 } $.
$$ \begin{aligned} \cancel{\frac{1}{3}}-x -\cancel{1} & = 0 ~~~ / \cdot \color{blue}{ 3 } \\[1 em] 1-3x-3 & = 0 \end{aligned} $$Step 2:
Combine like terms:
$$ \color{blue}{1} -3x \color{blue}{-3} = -3x \color{blue}{-2} $$Step 3:
$$ \begin{aligned} -3x-2 & = 0 \\[1 em] -3 \cdot x & = 2 \\[1 em] x & = \frac{ 2 }{ -3 } \end{aligned} $$