Find Where Undefined/Discontinuous h(x)=(x^2+4x-32)/(x^2-8x+16)

$h (x) = \frac{x^{2} + 4 x - 32}{x^{2} - 8 x + 16}$

Set the denominator in $\frac{x^{2} + 4 x - 32}{x^{2} - 8 x + 16}$ equal to $0$ to find where the expression is undefined.

$x^{2} - 8 x + 16 = 0$

Solve for $x$ .

Factor using the perfect square rule.

Rewrite $16$ as $4^{2}$ .

$x^{2} - 8 x + 4^{2} = 0$

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

$8 x = 2 \cdot x \cdot 4$

Rewrite the polynomial.

$x^{2} - 2 \cdot x \cdot 4 + 4^{2} = 0$

Factor using the perfect square trinomial rule $a^{2} - 2 a b + b^{2} = {(a - b)}^{2}$ , where $a = x$ and $b = 4$ .

${(x - 4)}^{2} = 0$

Set the $x - 4$ equal to $0$ .

$x - 4 = 0$

Add $4$ to both sides of the equation.

$x = 4$