Cancel the Common Factors

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

Step 1

Replace all occurrences of $+$ $-$ with a single $-$ . A plus sign followed by a minus sign has the same mathematical meaning as a single minus sign because $1 \cdot - 1 = - 1$

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

Step 2

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

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Step 2.1

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

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

Step 2.2

Factor $x$ out of $- 2 x$ .

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

Step 2.3

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

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

Step 3

Factor $x$ out of $x^{3} - 2 x^{2} + 4 x$ .

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Step 3.1

Factor $x$ out of $x^{3}$ .

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

Step 3.2

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

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

Step 3.3

Factor $x$ out of $4 x$ .

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

Step 3.4

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

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

Step 3.5

Factor $x$ out of $x (x^{2} - 2 x) + x \cdot 4$ .

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

Step 4

Reduce the expression $\frac{x (x - 2)}{x (x^{2} - 2 x + 4)}$ by cancelling the common factors.

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Step 4.1

Cancel the common factor.

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

Step 4.2

Rewrite the expression.

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

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