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

Step 1: Write $ 1 $ 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 second fraction by $\color{blue}{x^2}$.

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