The expression you've provided is:

$\frac{x^2 - x - 6}{7} \cdot \frac{7}{x+2}$

Let's simplify this step by step:

1. Factor the quadratic expression $x^2 - x - 6$: $x^2 - x - 6 = (x - 3)(x + 2)$

2. Now, substitute this factorization into the expression: $\frac{(x - 3)(x + 2)}{7} \cdot \frac{7}{x + 2}$

3. Cancel out the common factors. The term $x+2$ appears in both the numerator and denominator, and the 7 in the numerator and denominator cancels out as well: $\frac{(x - 3) \cancel{(x + 2)}}{\cancel{7}} \cdot \frac{\cancel{7}}{\cancel{x + 2}} = x - 3$

So, the simplified form of the expression is:

$x - 3$

Would you like more details or have any questions? Here are 5 related questions to consider:

1. How do you factor quadratic expressions like $x^2 - x - 6$?
2. What happens when terms cancel out in rational expressions?
3. Can all quadratic expressions be factored into two binomials?
4. How would you handle more complex rational expressions?
5. How does multiplying fractions simplify the process of solving algebraic equations?

Tip: Always check for common factors in both the numerator and denominator when simplifying rational expressions.