Simplify (3x-6)/(x^2-4x+4)

$\frac{3 x - 6}{x^{2} - 4 x + 4}$

Step 1

Factor $3$ out of $3 x - 6$ .

Factor $3$ out of $3 x$ .

$\frac{3 (x) - 6}{x^{2} - 4 x + 4}$

Factor $3$ out of $- 6$ .

$\frac{3 x + 3 \cdot - 2}{x^{2} - 4 x + 4}$

Factor $3$ out of $3 x + 3 \cdot - 2$ .

$\frac{3 (x - 2)}{x^{2} - 4 x + 4}$

Step 2

Factor using the perfect square rule.

Rewrite $4$ as $2^{2}$ .

$\frac{3 (x - 2)}{x^{2} - 4 x + 2^{2}}$

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

$4 x = 2 \cdot x \cdot 2$

Rewrite the polynomial.

$\frac{3 (x - 2)}{x^{2} - 2 \cdot x \cdot 2 + 2^{2}}$

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

$\frac{3 (x - 2)}{{(x - 2)}^{2}}$

Step 3

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

Factor $x - 2$ out of $3 (x - 2)$ .

$\frac{(x - 2) \cdot 3}{{(x - 2)}^{2}}$

Cancel the common factors.

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

$\frac{(x - 2) \cdot 3}{(x - 2) (x - 2)}$

Cancel the common factor.

$\frac{(x - 2) \cdot 3}{(x - 2) (x - 2)}$

Rewrite the expression.

$\frac{3}{x - 2}$