Trigonometry Examples

$\frac{x^{3} - 3 x^{2} + 6 x - 18}{x^{2} - 4 x}$

Step 1

Simplify the numerator.

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Step 1.1

Factor out the greatest common factor from each group.

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Step 1.1.1

Group the first two terms and the last two terms.

$\frac{(x^{3} - 3 x^{2}) + 6 x - 18}{x^{2} - 4 x}$

Step 1.1.2

Factor out the greatest common factor (GCF) from each group.

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

Step 1.2

Factor the polynomial by factoring out the greatest common factor, $x - 3$ .

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

Step 2

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

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Step 2.1

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

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

Step 2.2

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

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

Step 2.3

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

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