Find the Excluded Values (v-5)/(v^2-10v+25)

$\frac{v - 5}{v^{2} - 10 v + 25}$

Step 1

Set the denominator in $\frac{v - 5}{v^{2} - 10 v + 25}$ equal to $0$ to find where the expression is undefined.

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

Step 2

Solve for $v$ .

Factor using the perfect square rule.

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

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

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

$10 v = 2 \cdot v \cdot 5$

Rewrite the polynomial.

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

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

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

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

$v - 5 = 0$

Add $5$ to both sides of the equation.

$v = 5$

Step 3