Simplify (v-5)/(v^2-10v+25)

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

Step 1

Factor using the perfect square rule.

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

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

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.

$\frac{v - 5}{v^{2} - 2 \cdot v \cdot 5 + 5^{2}}$

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

$\frac{v - 5}{{(v - 5)}^{2}}$

Step 2

Cancel the common factor of $v - 5$ and ${(v - 5)}^{2}$ .

Multiply by $1$ .

$\frac{(v - 5) \cdot 1}{{(v - 5)}^{2}}$

Cancel the common factors.

Factor $v - 5$ out of ${(v - 5)}^{2}$ .

$\frac{(v - 5) \cdot 1}{(v - 5) (v - 5)}$

Cancel the common factor.

$\frac{(v - 5) \cdot 1}{(v - 5) (v - 5)}$

Rewrite the expression.

$\frac{1}{v - 5}$