Simplify (5x^2+15x)/(x^2+6x+9)

$\frac{5 x^{2} + 15 x}{x^{2} + 6 x + 9}$

Step 1

Factor $5 x$ out of $5 x^{2} + 15 x$ .

Factor $5 x$ out of $5 x^{2}$ .

$\frac{5 x (x) + 15 x}{x^{2} + 6 x + 9}$

Factor $5 x$ out of $15 x$ .

$\frac{5 x (x) + 5 x (3)}{x^{2} + 6 x + 9}$

Factor $5 x$ out of $5 x (x) + 5 x (3)$ .

$\frac{5 x (x + 3)}{x^{2} + 6 x + 9}$

Step 2

Factor using the perfect square rule.

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

$\frac{5 x (x + 3)}{x^{2} + 6 x + 3^{2}}$

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

$6 x = 2 \cdot x \cdot 3$

Rewrite the polynomial.

$\frac{5 x (x + 3)}{x^{2} + 2 \cdot x \cdot 3 + 3^{2}}$

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

$\frac{5 x (x + 3)}{{(x + 3)}^{2}}$

Step 3

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

Factor $x + 3$ out of $5 x (x + 3)$ .

$\frac{(x + 3) (5 x)}{{(x + 3)}^{2}}$

Cancel the common factors.

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

$\frac{(x + 3) (5 x)}{(x + 3) (x + 3)}$

Cancel the common factor.

$\frac{(x + 3) (5 x)}{(x + 3) (x + 3)}$

Rewrite the expression.

$\frac{5 x}{x + 3}$