Algebra Examples

$\frac{5 x - 5}{3 x} \cdot \frac{9}{6 x - 6}$

Step 1

Factor $5$ out of $5 x - 5$ .

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Step 1.1

Factor $5$ out of $5 x$ .

$\frac{5 (x) - 5}{3 x} \cdot \frac{9}{6 x - 6}$

Step 1.2

Factor $5$ out of $- 5$ .

$\frac{5 (x) + 5 (- 1)}{3 x} \cdot \frac{9}{6 x - 6}$

Step 1.3

Factor $5$ out of $5 (x) + 5 (- 1)$ .

$\frac{5 (x - 1)}{3 x} \cdot \frac{9}{6 x - 6}$

Step 2

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

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Step 2.1

Factor $6$ out of $6 x$ .

$\frac{5 (x - 1)}{3 x} \cdot \frac{9}{6 (x) - 6}$

Step 2.2

Factor $6$ out of $- 6$ .

$\frac{5 (x - 1)}{3 x} \cdot \frac{9}{6 (x) + 6 (- 1)}$

Step 2.3

Factor $6$ out of $6 (x) + 6 (- 1)$ .

$\frac{5 (x - 1)}{3 x} \cdot \frac{9}{6 (x - 1)}$

Step 3

Cancel the common factor of $x - 1$ .

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Step 3.1

Factor $x - 1$ out of $5 (x - 1)$ .

$\frac{(x - 1) \cdot 5}{3 x} \cdot \frac{9}{6 (x - 1)}$

Step 3.2

Factor $x - 1$ out of $6 (x - 1)$ .

$\frac{(x - 1) \cdot 5}{3 x} \cdot \frac{9}{(x - 1) \cdot 6}$

Step 3.3

Cancel the common factor.

$\frac{(x - 1) \cdot 5}{3 x} \cdot \frac{9}{(x - 1) \cdot 6}$

Step 3.4

Rewrite the expression.

$\frac{5}{3 x} \cdot \frac{9}{6}$

Step 4

Cancel the common factor of $3$ .

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Step 4.1

Factor $3$ out of $3 x$ .

$\frac{5}{3 (x)} \cdot \frac{9}{6}$

Step 4.2

Factor $3$ out of $9$ .

$\frac{5}{3 (x)} \cdot \frac{3 (3)}{6}$

Step 4.3

Cancel the common factor.

$\frac{5}{3 x} \cdot \frac{3 \cdot 3}{6}$

Step 4.4

Rewrite the expression.

$\frac{5}{x} \cdot \frac{3}{6}$

Step 5

Multiply $\frac{5}{x}$ by $\frac{3}{6}$ .

$\frac{5 \cdot 3}{x \cdot 6}$

Step 6

Multiply $5$ by $3$ .

$\frac{15}{x \cdot 6}$

Step 7

Cancel the common factor of $15$ and $6$ .

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Step 7.1

Factor $3$ out of $15$ .

$\frac{3 (5)}{x \cdot 6}$

Step 7.2

Cancel the common factors.

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Step 7.2.1

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

$\frac{3 (5)}{3 (x \cdot 2)}$

Step 7.2.2

Cancel the common factor.

$\frac{3 \cdot 5}{3 (x \cdot 2)}$

Step 7.2.3

Rewrite the expression.

$\frac{5}{x \cdot 2}$

Step 8

Move $2$ to the left of $x$ .

$\frac{5}{2 x}$