Find Where Undefined/Discontinuous y=(5x+6)/(x^2+6x+9)

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

Step 1

Set the denominator in $\frac{5 x + 6}{x^{2} + 6 x + 9}$ equal to $0$ to find where the expression is undefined.

$x^{2} + 6 x + 9 = 0$

Step 2

Solve for $x$ .

Factor using the perfect square rule.

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

$x^{2} + 6 x + 3^{2} = 0$

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.

$x^{2} + 2 \cdot x \cdot 3 + 3^{2} = 0$

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

${(x + 3)}^{2} = 0$

Set the $x + 3$ equal to $0$ .

$x + 3 = 0$

Subtract $3$ from both sides of the equation.

$x = - 3$

Step 3