Multiply $3$ by $ \dfrac{y}{x} $ to get $ \dfrac{ 3y }{ x } $.

Step 1: Write $ 3 $ as a fraction by putting $ \color{red}{1} $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} 3 \cdot \frac{y}{x} & \xlongequal{\text{Step 1}} \frac{3}{\color{red}{1}} \cdot \frac{y}{x} \xlongequal{\text{Step 2}} \frac{ 3 \cdot y }{ 1 \cdot x } \xlongequal{\text{Step 3}} \frac{ 3y }{ x } \end{aligned} $$

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

Step 1: Write $ 3-2x $ 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 $\color{blue}{ x }$.

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

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

Step 1: Write $ 2y $ 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 $\color{blue}{x}$.

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