Find the Excluded Values (24+5n-n^2)/(n^2-16n+64)

$\frac{24 + 5 n - n^{2}}{n^{2} - 16 n + 64}$

Step 1

Set the denominator in $\frac{24 + 5 n - n^{2}}{n^{2} - 16 n + 64}$ equal to $0$ to find where the expression is undefined.

$n^{2} - 16 n + 64 = 0$

Step 2

Solve for $n$ .

Factor using the perfect square rule.

Rewrite $64$ as $8^{2}$ .

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

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

$16 n = 2 \cdot n \cdot 8$

Rewrite the polynomial.

$n^{2} - 2 \cdot n \cdot 8 + 8^{2} = 0$

Factor using the perfect square trinomial rule $a^{2} - 2 a b + b^{2} = {(a - b)}^{2}$ , where $a = n$ and $b = 8$ .

${(n - 8)}^{2} = 0$

Set the $n - 8$ equal to $0$ .

$n - 8 = 0$

Add $8$ to both sides of the equation.

$n = 8$

Step 3