Trigonometry Examples

$\frac{x^{2} - 5 x + 6}{x^{2} - 4 x} \cdot \frac{x - 4}{x - 3}$

Step 1

Factor $x^{2} - 5 x + 6$ using the AC method.

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Step 1.1

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $6$ and whose sum is $- 5$ .

$- 3, - 2$

Step 1.2

Write the factored form using these integers.

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

Step 2

Simplify terms.

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Step 2.1

Factor $x$ out of $x^{2} - 4 x$ .

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Step 2.1.1

Factor $x$ out of $x^{2}$ .

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

Step 2.1.2

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

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

Step 2.1.3

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

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

Step 2.2

Cancel the common factor of $x - 3$ .

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Step 2.2.1

Cancel the common factor.

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

Step 2.2.2

Rewrite the expression.

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

Step 2.3

Cancel the common factor of $x - 4$ .

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Step 2.3.1

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

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

Step 2.3.2

Cancel the common factor.

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

Step 2.3.3

Rewrite the expression.

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