Subtract $ \dfrac{x^2}{y^2} $ from $ xy^3 $ to get $ \dfrac{ \color{purple}{ xy^5-x^2 } }{ y^2 }$.

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

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

$$ \begin{aligned} xy^3- \frac{x^2}{y^2} & \xlongequal{\text{Step 1}} \frac{xy^3}{\color{red}{1}} - \frac{x^2}{y^2} = \frac{ xy^3 \cdot \color{blue}{ y^2 }}{ 1 \cdot \color{blue}{ y^2 }} - \frac{ x^2 }{ y^2 } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ xy^5 } }{ y^2 } - \frac{ \color{purple}{ x^2 } }{ y^2 }=\frac{ \color{purple}{ xy^5-x^2 } }{ y^2 } \end{aligned} $$