Subtract $ \dfrac{6}{x^2} $ from $ \dfrac{1}{x} $ to get $ \dfrac{ \color{purple}{ x^2-6x } }{ x^3 }$.

To subtract raitonal expressions, both fractions must have the same denominator.
We can create a common denominator by multiplying the first fraction by $ \color{blue}{ x^2 }$ and the second by $\color{blue}{ x }$.

$$ \begin{aligned} \frac{1}{x} - \frac{6}{x^2} & = \frac{ 1 \cdot \color{blue}{ x^2 }}{ x \cdot \color{blue}{ x^2 }} - \frac{ 6 \cdot \color{blue}{ x }}{ x^2 \cdot \color{blue}{ x }} = \\[1ex] &=\frac{ \color{purple}{ x^2 } }{ x^3 } - \frac{ \color{purple}{ 6x } }{ x^3 }=\frac{ \color{purple}{ x^2-6x } }{ x^3 } \end{aligned} $$