Precalculus Examples

$\frac{4 x - 4}{x} \cdot \frac{2 x^{2}}{9 x - 9}$

Step 1

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

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Step 1.1

Factor $4$ out of $4 x$ .

$\frac{4 (x) - 4}{x} \cdot \frac{2 x^{2}}{9 x - 9}$

Step 1.2

Factor $4$ out of $- 4$ .

$\frac{4 (x) + 4 (- 1)}{x} \cdot \frac{2 x^{2}}{9 x - 9}$

Step 1.3

Factor $4$ out of $4 (x) + 4 (- 1)$ .

$\frac{4 (x - 1)}{x} \cdot \frac{2 x^{2}}{9 x - 9}$

Step 2

Factor $9$ out of $9 x - 9$ .

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Step 2.1

Factor $9$ out of $9 x$ .

$\frac{4 (x - 1)}{x} \cdot \frac{2 x^{2}}{9 (x) - 9}$

Step 2.2

Factor $9$ out of $- 9$ .

$\frac{4 (x - 1)}{x} \cdot \frac{2 x^{2}}{9 (x) + 9 (- 1)}$

Step 2.3

Factor $9$ out of $9 (x) + 9 (- 1)$ .

$\frac{4 (x - 1)}{x} \cdot \frac{2 x^{2}}{9 (x - 1)}$

Step 3

Combine.

$\frac{4 (x - 1) (2 x^{2})}{x (9 (x - 1))}$

Step 4

Cancel the common factor of $x - 1$ .

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Step 4.1

Cancel the common factor.

$\frac{4 (x - 1) (2 x^{2})}{x (9 (x - 1))}$

Step 4.2

Rewrite the expression.

$\frac{4 (2 x^{2})}{x \cdot (9)}$

Step 5

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

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Step 5.1

Factor $x$ out of $4 (2 x^{2})$ .

$\frac{x (4 (2 x))}{x \cdot (9)}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $x$ out of $x \cdot (9)$ .

$\frac{x (4 (2 x))}{x (9)}$

Step 5.2.2

Cancel the common factor.

$\frac{x (4 (2 x))}{x \cdot 9}$

Step 5.2.3

Rewrite the expression.

$\frac{4 (2 x)}{9}$

Step 6

Multiply $4$ by $2$ .

$\frac{8 x}{9}$