Add $ \dfrac{70}{b} $ and $ 3a $ to get $ \dfrac{ \color{purple}{ 3ab+70 } }{ b }$.

Step 1: Write $ 3a $ 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 $\color{blue}{b}$.

$$ \begin{aligned} \frac{70}{b} +3a & \xlongequal{\text{Step 1}} \frac{70}{b} + \frac{3a}{\color{red}{1}} = \frac{ 70 }{ b } + \frac{ 3a \cdot \color{blue}{ b }}{ 1 \cdot \color{blue}{ b }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 70 } }{ b } + \frac{ \color{purple}{ 3ab } }{ b }=\frac{ \color{purple}{ 3ab+70 } }{ b } \end{aligned} $$

Subtract $10b$ from $ \dfrac{3ab+70}{b} $ to get $ \dfrac{ \color{purple}{ 3ab-10b^2+70 } }{ b }$.

Step 1: Write $ 10b $ 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 $\color{blue}{b}$.

$$ \begin{aligned} \frac{3ab+70}{b} -10b & \xlongequal{\text{Step 1}} \frac{3ab+70}{b} - \frac{10b}{\color{red}{1}} = \frac{ 3ab+70 }{ b } - \frac{ 10b \cdot \color{blue}{ b }}{ 1 \cdot \color{blue}{ b }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 3ab+70 } }{ b } - \frac{ \color{purple}{ 10b^2 } }{ b }=\frac{ \color{purple}{ 3ab-10b^2+70 } }{ b } \end{aligned} $$