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

Step 1: Write $ x^3 $ 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 $\color{blue}{ y }$.

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