Divide $ \dfrac{x^2+2x-80}{x+2} $ by $ \dfrac{x^2-100}{x-2} $ to get $ \dfrac{x^2-10x+16}{x^2-8x-20} $.

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.

$$ \begin{aligned} \frac{ \frac{x^2+2x-80}{x+2} }{ \frac{\color{blue}{x^2-100}}{\color{blue}{x-2}} } & \xlongequal{\text{Step 1}} \frac{x^2+2x-80}{x+2} \cdot \frac{\color{blue}{x-2}}{\color{blue}{x^2-100}} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \left( x-8 \right) \cdot \color{blue}{ \left( x+10 \right) } }{ x+2 } \cdot \frac{ x-2 }{ \left( x-10 \right) \cdot \color{blue}{ \left( x+10 \right) } } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ x-8 }{ x+2 } \cdot \frac{ x-2 }{ x-10 } \xlongequal{\text{Step 4}} \frac{ \left( x-8 \right) \cdot \left( x-2 \right) }{ \left( x+2 \right) \cdot \left( x-10 \right) } = \\[1ex] & \xlongequal{\text{Step 5}} \frac{ x^2-2x-8x+16 }{ x^2-10x+2x-20 } = \frac{x^2-10x+16}{x^2-8x-20} \end{aligned} $$