Multiply $x^2$ by $ \dfrac{y^5}{3} $ to get $ \dfrac{ x^2y^5 }{ 3 } $.

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

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

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

Subtract $ \dfrac{x^2y^5}{3} $ from $ 7x-3 $ to get $ \dfrac{ \color{purple}{ -x^2y^5+21x-9 } }{ 3 }$.

Step 1: Write $ 7x-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 $\color{blue}{ 3 }$.

$$ \begin{aligned} 7x-3- \frac{x^2y^5}{3} & \xlongequal{\text{Step 1}} \frac{7x-3}{\color{red}{1}} - \frac{x^2y^5}{3} = \frac{ \left( 7x-3 \right) \cdot \color{blue}{ 3 }}{ 1 \cdot \color{blue}{ 3 }} - \frac{ x^2y^5 }{ 3 } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 21x-9 } }{ 3 } - \frac{ \color{purple}{ x^2y^5 } }{ 3 }=\frac{ \color{purple}{ -x^2y^5+21x-9 } }{ 3 } \end{aligned} $$