Divide $ \dfrac{2x-6}{3x+6} $ by $ 5x-15 $ to get $ \dfrac{ 2 }{ 15x+30 } $.

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.

$$ \begin{aligned} \frac{ \frac{2x-6}{3x+6} }{5x-15} & \xlongequal{\text{Step 1}} \frac{2x-6}{3x+6} \cdot \frac{\color{blue}{1}}{\color{blue}{5x-15}} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ 2 \cdot \color{blue}{ \left( x-3 \right) } }{ 3x+6 } \cdot \frac{ 1 }{ 5 \cdot \color{blue}{ \left( x-3 \right) } } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 2 }{ 3x+6 } \cdot \frac{ 1 }{ 5 } \xlongequal{\text{Step 4}} \frac{ 2 \cdot 1 }{ \left( 3x+6 \right) \cdot 5 } \xlongequal{\text{Step 5}} \frac{ 2 }{ 15x+30 } \end{aligned} $$