Find Where Undefined/Discontinuous (5k^2-50k+45)/(k^2-18k+81)

$\frac{5 k^{2} - 50 k + 45}{k^{2} - 18 k + 81}$

Step 1

Set the denominator in $\frac{5 k^{2} - 50 k + 45}{k^{2} - 18 k + 81}$ equal to $0$ to find where the expression is undefined.

$k^{2} - 18 k + 81 = 0$

Step 2

Solve for $k$ .

Factor using the perfect square rule.

Rewrite $81$ as $9^{2}$ .

$k^{2} - 18 k + 9^{2} = 0$

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

$18 k = 2 \cdot k \cdot 9$

Rewrite the polynomial.

$k^{2} - 2 \cdot k \cdot 9 + 9^{2} = 0$

Factor using the perfect square trinomial rule $a^{2} - 2 a b + b^{2} = {(a - b)}^{2}$ , where $a = k$ and $b = 9$ .

${(k - 9)}^{2} = 0$

Set the $k - 9$ equal to $0$ .

$k - 9 = 0$

Add $9$ to both sides of the equation.

$k = 9$

Step 3