Multiply $ \dfrac{2x+14}{x+1} $ by $ \dfrac{x^2-1}{6x^2+42x} $ to get $ \dfrac{ x-1 }{ 3x } $.

Step 1: Factor numerators and denominators.

Step 2: Cancel common factors.

Step 3: Multiply numerators and denominators.

Step 4: Simplify numerator and denominator.

$$ \begin{aligned} \frac{2x+14}{x+1} \cdot \frac{x^2-1}{6x^2+42x} & \xlongequal{\text{Step 1}} \frac{ 1 \cdot \color{blue}{ \left( 2x+14 \right) } }{ 1 \cdot \color{red}{ \left( x+1 \right) } } \cdot \frac{ \left( x-1 \right) \cdot \color{red}{ \left( x+1 \right) } }{ 3x \cdot \color{blue}{ \left( 2x+14 \right) } } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ 1 }{ 1 } \cdot \frac{ x-1 }{ 3x } \xlongequal{\text{Step 3}} \frac{ 1 \cdot \left( x-1 \right) }{ 1 \cdot 3x } \xlongequal{\text{Step 4}} \frac{ x-1 }{ 3x } \end{aligned} $$