Simplify ((x-5)/6)(18/(x^2-10x+25))

$(\frac{x - 5}{6}) (\frac{18}{x^{2} - 10 x + 25})$

Step 1

Factor using the perfect square rule.

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

$\frac{x - 5}{6} \cdot \frac{18}{x^{2} - 10 x + 5^{2}}$

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

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

Rewrite the polynomial.

$\frac{x - 5}{6} \cdot \frac{18}{x^{2} - 2 \cdot x \cdot 5 + 5^{2}}$

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

$\frac{x - 5}{6} \cdot \frac{18}{{(x - 5)}^{2}}$

Step 2

Reduce the expression by cancelling the common factors.

Cancel the common factor of $x - 5$ .

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

$\frac{x - 5}{6} \cdot \frac{18}{(x - 5) (x - 5)}$

Cancel the common factor.

$\frac{x - 5}{6} \cdot \frac{18}{(x - 5) (x - 5)}$

Rewrite the expression.

$\frac{1}{6} \cdot \frac{18}{x - 5}$

Cancel the common factor of $6$ .

Factor $6$ out of $18$ .

$\frac{1}{6} \cdot \frac{6 (3)}{x - 5}$

Cancel the common factor.

$\frac{1}{6} \cdot \frac{6 \cdot 3}{x - 5}$

Rewrite the expression.

$\frac{3}{x - 5}$