Multiply $2$ by $ \dfrac{x}{y} $ to get $ \dfrac{ 2x }{ y } $.

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

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

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

Add $1$ and $ \dfrac{2x}{y} $ to get $ \dfrac{ \color{purple}{ 2x+y } }{ y }$.

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 first fraction by $\color{blue}{ y }$.

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

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

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}{ y^2 }$ and the second by $\color{blue}{ y }$.

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