1. **State the problems:** We have two problems to solve: - Simplify the expression $(3x + 2y)(3x - y)$. - Simplify the rational expression $\frac{n + 2}{n^2 - n - 6}$. 2. **Simplify $(3x + 2y)(3x - y)$:** Use the distributive property (FOIL method) to expand: $$ (3x + 2y)(3x - y) = 3x \cdot 3x + 3x \cdot (-y) + 2y \cdot 3x + 2y \cdot (-y) $$ Calculate each term: $$ = 9x^2 - 3xy + 6xy - 2y^2 $$ Combine like terms $-3xy + 6xy = 3xy$: $$ = 9x^2 + 3xy - 2y^2 $$ 3. **Simplify $\frac{n + 2}{n^2 - n - 6}$:** First, factor the denominator: $$ n^2 - n - 6 = (n - 3)(n + 2) $$ Rewrite the expression: $$ \frac{n + 2}{(n - 3)(n + 2)} $$ Cancel the common factor $n + 2$ (assuming $n \neq -2$): $$ \frac{\cancel{n + 2}}{(n - 3)\cancel{(n + 2)}} = \frac{1}{n - 3} $$ 4. **Final answers:** - $(3x + 2y)(3x - y) = 9x^2 + 3xy - 2y^2$ - $\frac{n + 2}{n^2 - n - 6} = \frac{1}{n - 3}$ (valid for $n \neq -2, 3$)