Find Where Undefined/Discontinuous (2x-10)/(x^2-10x+25)

$\frac{2 x - 10}{x^{2} - 10 x + 25}$

Step 1

Set the denominator in $\frac{2 x - 10}{x^{2} - 10 x + 25}$ equal to $0$ to find where the expression is undefined.

$x^{2} - 10 x + 25 = 0$

Step 2

Solve for $x$ .

Factor using the perfect square rule.

Rewrite $25$ as $5^{2}$ .

$x^{2} - 10 x + 5^{2} = 0$

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

$10 x = 2 \cdot x \cdot 5$

Rewrite the polynomial.

$x^{2} - 2 \cdot x \cdot 5 + 5^{2} = 0$

Factor using the perfect square trinomial rule $a^{2} - 2 a b + b^{2} = {(a - b)}^{2}$ , where $a = x$ and $b = 5$ .

${(x - 5)}^{2} = 0$

Set the $x - 5$ equal to $0$ .

$x - 5 = 0$

Add $5$ to both sides of the equation.

$x = 5$

Step 3