Add $4x^2-6x$ and $ \dfrac{1}{x} $ to get $ \dfrac{ \color{purple}{ 4x^3-6x^2+1 } }{ x }$.

Step 1: Write $ 4x^2-6x $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator.

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

$$ \begin{aligned} 4x^2-6x+ \frac{1}{x} & \xlongequal{\text{Step 1}} \frac{4x^2-6x}{\color{red}{1}} + \frac{1}{x} = \frac{ \left( 4x^2-6x \right) \cdot \color{blue}{ x }}{ 1 \cdot \color{blue}{ x }} + \frac{ 1 }{ x } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 4x^3-6x^2 } }{ x } + \frac{ \color{purple}{ 1 } }{ x }=\frac{ \color{purple}{ 4x^3-6x^2+1 } }{ x } \end{aligned} $$