Subtract $ \dfrac{a^2}{a^2} $ from $ 15+2a $ to get $ \dfrac{ \color{purple}{ 2a^3+14a^2 } }{ a^2 }$.

Step 1: Write $ 15+2a $ 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 $\color{blue}{ a^2 }$.

$$ \begin{aligned} 15+2a- \frac{a^2}{a^2} & \xlongequal{\text{Step 1}} \frac{15+2a}{\color{red}{1}} - \frac{a^2}{a^2} = \frac{ \left( 15+2a \right) \cdot \color{blue}{ a^2 }}{ 1 \cdot \color{blue}{ a^2 }} - \frac{ a^2 }{ a^2 } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 15a^2+2a^3 } }{ a^2 } - \frac{ \color{purple}{ a^2 } }{ a^2 }=\frac{ \color{purple}{ 2a^3+14a^2 } }{ a^2 } \end{aligned} $$

Add $ \dfrac{2a^3+14a^2}{a^2} $ and $ a $ to get $ \dfrac{ \color{purple}{ 3a^3+14a^2 } }{ a^2 }$.

Step 1: Write $ a $ 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 $\color{blue}{a^2}$.

$$ \begin{aligned} \frac{2a^3+14a^2}{a^2} +a & \xlongequal{\text{Step 1}} \frac{2a^3+14a^2}{a^2} + \frac{a}{\color{red}{1}} = \frac{ 2a^3+14a^2 }{ a^2 } + \frac{ a \cdot \color{blue}{ a^2 }}{ 1 \cdot \color{blue}{ a^2 }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 2a^3+14a^2 } }{ a^2 } + \frac{ \color{purple}{ a^3 } }{ a^2 }=\frac{ \color{purple}{ 3a^3+14a^2 } }{ a^2 } \end{aligned} $$

Subtract $30$ from $ \dfrac{3a^3+14a^2}{a^2} $ to get $ \dfrac{ \color{purple}{ 3a^3-16a^2 } }{ a^2 }$.

Step 1: Write $ 30 $ 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 second fraction by $\color{blue}{a^2}$.

$$ \begin{aligned} \frac{3a^3+14a^2}{a^2} -30 & \xlongequal{\text{Step 1}} \frac{3a^3+14a^2}{a^2} - \frac{30}{\color{red}{1}} = \frac{ 3a^3+14a^2 }{ a^2 } - \frac{ 30 \cdot \color{blue}{ a^2 }}{ 1 \cdot \color{blue}{ a^2 }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 3a^3+14a^2 } }{ a^2 } - \frac{ \color{purple}{ 30a^2 } }{ a^2 }=\frac{ \color{purple}{ 3a^3-16a^2 } }{ a^2 } \end{aligned} $$