Simplify (x^2-12x+36)/(4x-24)

$\frac{x^{2} - 12 x + 36}{4 x - 24}$

Step 1

Factor using the perfect square rule.

Rewrite $36$ as $6^{2}$ .

$\frac{x^{2} - 12 x + 6^{2}}{4 x - 24}$

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

$12 x = 2 \cdot x \cdot 6$

Rewrite the polynomial.

$\frac{x^{2} - 2 \cdot x \cdot 6 + 6^{2}}{4 x - 24}$

Factor using the perfect square trinomial rule $a^{2} - 2 a b + b^{2} = {(a - b)}^{2}$ , where $a = x$ and $b = 6$ .

$\frac{{(x - 6)}^{2}}{4 x - 24}$

Step 2

Simplify terms.

Factor $4$ out of $4 x - 24$ .

Factor $4$ out of $4 x$ .

$\frac{{(x - 6)}^{2}}{4 (x) - 24}$

Factor $4$ out of $- 24$ .

$\frac{{(x - 6)}^{2}}{4 x + 4 \cdot - 6}$

Factor $4$ out of $4 x + 4 \cdot - 6$ .

$\frac{{(x - 6)}^{2}}{4 (x - 6)}$

Cancel the common factor of ${(x - 6)}^{2}$ and $x - 6$ .

Factor $x - 6$ out of ${(x - 6)}^{2}$ .

$\frac{(x - 6) (x - 6)}{4 (x - 6)}$

Cancel the common factors.

Factor $x - 6$ out of $4 (x - 6)$ .

$\frac{(x - 6) (x - 6)}{(x - 6) \cdot 4}$

Cancel the common factor.

$\frac{(x - 6) (x - 6)}{(x - 6) \cdot 4}$

Rewrite the expression.

$\frac{x - 6}{4}$