Simplify numerator

$$ \color{blue}{x} \color{blue}{-2x} +1 = \color{blue}{-x} +1 $$

Divide $ \dfrac{-x+1}{12} $ by $ x^2-1 $ to get $ \dfrac{ -1 }{ 12x+12 } $.

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.

$$ \begin{aligned} \frac{ \frac{-x+1}{12} }{x^2-1} & \xlongequal{\text{Step 1}} \frac{-x+1}{12} \cdot \frac{\color{blue}{1}}{\color{blue}{x^2-1}} \xlongequal{\text{Step 2}} \frac{ \left( -1 \right) \cdot \color{blue}{ \left( x-1 \right) } }{ 12 } \cdot \frac{ 1 }{ \left( x+1 \right) \cdot \color{blue}{ \left( x-1 \right) } } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ -1 }{ 12 } \cdot \frac{ 1 }{ x+1 } \xlongequal{\text{Step 4}} \frac{ \left( -1 \right) \cdot 1 }{ 12 \cdot \left( x+1 \right) } = \\[1ex] & \xlongequal{\text{Step 5}} \frac{ -1 }{ 12x+12 } \end{aligned} $$

Divide $ \dfrac{-1}{12x+12} $ by $ 6 $ to get $ \dfrac{ -1 }{ 72x+72 } $.

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

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} \frac{ \frac{-1}{12x+12} }{6} & \xlongequal{\text{Step 1}} \frac{-1}{12x+12} \cdot \frac{\color{blue}{1}}{\color{blue}{6}} \xlongequal{\text{Step 2}} \frac{ \left( -1 \right) \cdot 1 }{ \left( 12x+12 \right) \cdot 6 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ -1 }{ 72x+72 } \end{aligned} $$