Find Where Undefined/Discontinuous f(x)=(x^2+5x+6)/(2x+16)

$f (x) = \frac{x^{2} + 5 x + 6}{2 x + 16}$

Step 1

Set the denominator in $\frac{x^{2} + 5 x + 6}{2 x + 16}$ equal to $0$ to find where the expression is undefined.

$2 x + 16 = 0$

Step 2

Solve for $x$ .

Subtract $16$ from both sides of the equation.

$2 x = - 16$

Divide each term in $2 x = - 16$ by $2$ and simplify.

Divide each term in $2 x = - 16$ by $2$ .

$\frac{2 x}{2} = \frac{- 16}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{- 16}{2}$

Divide $x$ by $1$ .

$x = \frac{- 16}{2}$

Simplify the right side.

Divide $- 16$ by $2$ .

$x = - 8$

Step 3