Trigonometry Examples

$\frac{x^{2} - 6 x + 9}{6 x - 18}$

Step 1

Factor using the perfect square rule.

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Step 1.1

Rewrite $9$ as $3^{2}$ .

$\frac{x^{2} - 6 x + 3^{2}}{6 x - 18}$

Step 1.2

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

$6 x = 2 \cdot x \cdot 3$

Step 1.3

Rewrite the polynomial.

$\frac{x^{2} - 2 \cdot x \cdot 3 + 3^{2}}{6 x - 18}$

Step 1.4

Factor using the perfect square trinomial rule $a^{2} - 2 a b + b^{2} = {(a - b)}^{2}$ , where $a = x$ and $b = 3$ .

$\frac{{(x - 3)}^{2}}{6 x - 18}$

Step 2

Simplify terms.

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Step 2.1

Factor $6$ out of $6 x - 18$ .

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Step 2.1.1

Factor $6$ out of $6 x$ .

$\frac{{(x - 3)}^{2}}{6 (x) - 18}$

Step 2.1.2

Factor $6$ out of $- 18$ .

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

Step 2.1.3

Factor $6$ out of $6 x + 6 \cdot - 3$ .

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

Step 2.2

Cancel the common factor of ${(x - 3)}^{2}$ and $x - 3$ .

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Step 2.2.1

Factor $x - 3$ out of ${(x - 3)}^{2}$ .

$\frac{(x - 3) (x - 3)}{6 (x - 3)}$

Step 2.2.2

Cancel the common factors.

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Step 2.2.2.1

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

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

Step 2.2.2.2

Cancel the common factor.

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

Step 2.2.2.3

Rewrite the expression.

$\frac{x - 3}{6}$