Divide $ \dfrac{2x^2-7x+3}{10x^3} $ by $ \dfrac{3-x}{5} $ to get $ \dfrac{ 10x-5 }{ -10x^3 } $.

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

Step 2: Factor numerators and denominators.

Step 3: Cancel common factors.

Step 4: Multiply numerators and denominators.

Step 5: Simplify numerator and denominator.

$$ \begin{aligned} \frac{ \frac{2x^2-7x+3}{10x^3} }{ \frac{\color{blue}{3-x}}{\color{blue}{5}} } & \xlongequal{\text{Step 1}} \frac{2x^2-7x+3}{10x^3} \cdot \frac{\color{blue}{5}}{\color{blue}{3-x}} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \left( 2x-1 \right) \cdot \color{blue}{ \left( x-3 \right) } }{ 10x^3 } \cdot \frac{ 5 }{ \left( -1 \right) \cdot \color{blue}{ \left( x-3 \right) } } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 2x-1 }{ 10x^3 } \cdot \frac{ 5 }{ -1 } \xlongequal{\text{Step 4}} \frac{ \left( 2x-1 \right) \cdot 5 }{ 10x^3 \cdot \left( -1 \right) } = \\[1ex] & \xlongequal{\text{Step 5}} \frac{ 10x-5 }{ -10x^3 } \end{aligned} $$