Find Where Undefined/Discontinuous (n^2-225)/(n^2+30n+225)

$\frac{n^{2} - 225}{n^{2} + 30 n + 225}$

Step 1

Set the denominator in $\frac{n^{2} - 225}{n^{2} + 30 n + 225}$ equal to $0$ to find where the expression is undefined.

$n^{2} + 30 n + 225 = 0$

Step 2

Solve for $n$ .

Factor using the perfect square rule.

Rewrite $225$ as $15^{2}$ .

$n^{2} + 30 n + 15^{2} = 0$

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

$30 n = 2 \cdot n \cdot 15$

Rewrite the polynomial.

$n^{2} + 2 \cdot n \cdot 15 + 15^{2} = 0$

Factor using the perfect square trinomial rule $a^{2} + 2 a b + b^{2} = {(a + b)}^{2}$ , where $a = n$ and $b = 15$ .

${(n + 15)}^{2} = 0$

Set the $n + 15$ equal to $0$ .

$n + 15 = 0$

Subtract $15$ from both sides of the equation.

$n = - 15$

Step 3