Simplify (a^2+6a)/(a+3)+9/(a+3)

$\frac{a^{2} + 6 a}{a + 3} + \frac{9}{a + 3}$

Step 1

Combine the numerators over the common denominator.

$\frac{a^{2} + 6 a + 9}{a + 3}$

Step 2

Factor using the perfect square rule.

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

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

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.

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

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

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

Step 3

Cancel the common factor of ${(a + 3)}^{2}$ and $a + 3$ .

Factor $a + 3$ out of ${(a + 3)}^{2}$ .

$\frac{(a + 3) (a + 3)}{a + 3}$

Cancel the common factors.

Multiply by $1$ .

$\frac{(a + 3) (a + 3)}{(a + 3) \cdot 1}$

Cancel the common factor.

$\frac{(a + 3) (a + 3)}{(a + 3) \cdot 1}$

Rewrite the expression.

$\frac{a + 3}{1}$

Divide $a + 3$ by $1$ .

$a + 3$