Divide $ \dfrac{x-6}{x+2} $ by $ \dfrac{x+8}{x+5} $ to get $ \dfrac{x^2-x-30}{x^2+10x+16} $.

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.

$$ \begin{aligned} \frac{ \frac{x-6}{x+2} }{ \frac{\color{blue}{x+8}}{\color{blue}{x+5}} } & \xlongequal{\text{Step 1}} \frac{x-6}{x+2} \cdot \frac{\color{blue}{x+5}}{\color{blue}{x+8}} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \left( x-6 \right) \cdot \left( x+5 \right) }{ \left( x+2 \right) \cdot \left( x+8 \right) } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ x^2+5x-6x-30 }{ x^2+8x+2x+16 } = \frac{x^2-x-30}{x^2+10x+16} \end{aligned} $$