Simplify $ \dfrac{x^2-6x}{x^2-36} $ to $ \dfrac{x}{x+6} $.

Factor both the denominator and the numerator, then cancel the common factor. $\color{blue}{x-6}$.

$$ \begin{aligned} \frac{x^2-6x}{x^2-36} & =\frac{ x \cdot \color{blue}{ \left( x-6 \right) }}{ \left( x+6 \right) \cdot \color{blue}{ \left( x-6 \right) }} = \\[1ex] &= \frac{x}{x+6} \end{aligned} $$

Multiply $ \dfrac{x}{x+6} $ by $ \dfrac{x+6}{x^2} $ to get $ \dfrac{ x }{ x^2 } $.

Step 1: Cancel $ \color{red}{ x+6 } $ in first and second fraction.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} \frac{x}{x+6} \cdot \frac{x+6}{x^2} & \xlongequal{\text{Step 1}} \frac{x}{\color{red}{1}} \cdot \frac{\color{red}{1}}{x^2} \xlongequal{\text{Step 2}} \frac{ x \cdot 1 }{ 1 \cdot x^2 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ x }{ x^2 } \end{aligned} $$