1. **State the problem:** Simplify the rational expressions: 5°) $\frac{a^2 + 4a + 4}{a^2 - 4}$ 6°) $\frac{4a^2 - 12a + 9}{4a^2 - 9}$ 2. **Recall the formulas and rules:** - Recognize perfect square trinomials: $x^2 + 2xy + y^2 = (x + y)^2$ - Difference of squares: $x^2 - y^2 = (x - y)(x + y)$ 3. **Simplify 5°:** Numerator: $a^2 + 4a + 4 = (a + 2)^2$ Denominator: $a^2 - 4 = (a - 2)(a + 2)$ So, $$\frac{a^2 + 4a + 4}{a^2 - 4} = \frac{(a + 2)^2}{(a - 2)(a + 2)}$$ Cancel common factor $a + 2$: $$\frac{\cancel{(a + 2)}(a + 2)}{(a - 2)\cancel{(a + 2)}} = \frac{a + 2}{a - 2}$$ 4. **Simplify 6°:** Numerator: $4a^2 - 12a + 9 = (2a - 3)^2$ Denominator: $4a^2 - 9 = (2a - 3)(2a + 3)$ So, $$\frac{4a^2 - 12a + 9}{4a^2 - 9} = \frac{(2a - 3)^2}{(2a - 3)(2a + 3)}$$ Cancel common factor $2a - 3$: $$\frac{\cancel{(2a - 3)}(2a - 3)}{\cancel{(2a - 3)}(2a + 3)} = \frac{2a - 3}{2a + 3}$$ **Final answers:** - 5°) $\frac{a + 2}{a - 2}$ - 6°) $\frac{2a - 3}{2a + 3}$