Find Where Undefined/Discontinuous (13z)/(z^2-4z+4)

$\frac{13 z}{z^{2} - 4 z + 4}$

Step 1

Set the denominator in $\frac{13 z}{z^{2} - 4 z + 4}$ equal to $0$ to find where the expression is undefined.

$z^{2} - 4 z + 4 = 0$

Step 2

Solve for $z$ .

Factor using the perfect square rule.

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

$z^{2} - 4 z + 2^{2} = 0$

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

$4 z = 2 \cdot z \cdot 2$

Rewrite the polynomial.

$z^{2} - 2 \cdot z \cdot 2 + 2^{2} = 0$

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

${(z - 2)}^{2} = 0$

Set the $z - 2$ equal to $0$ .

$z - 2 = 0$

Add $2$ to both sides of the equation.

$z = 2$

Step 3