Subtract $30j$ from $ \dfrac{-3}{20} $ to get $ \dfrac{ \color{purple}{ -600j-3 } }{ 20 }$.

Step 1: Write $ 30j $ 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 $\color{blue}{20}$.

$$ \begin{aligned} \frac{-3}{20} -30j & \xlongequal{\text{Step 1}} \frac{-3}{20} - \frac{30j}{\color{red}{1}} = \frac{ -3 }{ 20 } - \frac{ 30j \cdot \color{blue}{ 20 }}{ 1 \cdot \color{blue}{ 20 }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ -3 } }{ 20 } - \frac{ \color{purple}{ 600j } }{ 20 }=\frac{ \color{purple}{ -600j-3 } }{ 20 } \end{aligned} $$

Divide $15j-2$ by $ \dfrac{-600j-3}{20} $ to get $ \dfrac{ 300j-40 }{ -600j-3 } $.

Step 1: To divide rational expressions, multiply the first fraction by the reciprocal of the second fraction.

Step 2: Write $ 15j-2 $ as a fraction by putting $ \color{red}{1} $ in the denominator.

Step 3: Multiply numerators and denominators.

Step 4: Simplify numerator and denominator.

$$ \begin{aligned} \frac{15j-2}{ \frac{\color{blue}{-600j-3}}{\color{blue}{20}} } & \xlongequal{\text{Step 1}} 15j-2 \cdot \frac{\color{blue}{20}}{\color{blue}{-600j-3}} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{15j-2}{\color{red}{1}} \cdot \frac{20}{-600j-3} \xlongequal{\text{Step 3}} \frac{ \left( 15j-2 \right) \cdot 20 }{ 1 \cdot \left( -600j-3 \right) } = \\[1ex] & \xlongequal{\text{Step 4}} \frac{ 300j-40 }{ -600j-3 } \end{aligned} $$