Simplify (a^2+6a+9)/(a^2+6a+15)

$\frac{a^{2} + 6 a + 9}{a^{2} + 6 a + 15}$

Rewrite $9$ as $3^{2}$ .

$\frac{a^{2} + 6 a + 3^{2}}{a^{2} + 6 a + 15}$

Check that the middle term is two times the product of the numbers being squared in the first term and third term.

$6 a = 2 \cdot a \cdot 3$

Rewrite the polynomial.

$\frac{a^{2} + 2 \cdot a \cdot 3 + 3^{2}}{a^{2} + 6 a + 15}$

Factor using the perfect square trinomial rule $a^{2} + 2 a b + b^{2} = {(a + b)}^{2}$ , where $a = a$ and $b = 3$ .

$\frac{{(a + 3)}^{2}}{a^{2} + 6 a + 15}$