Algebra Examples

$\frac{5 x - 10}{6} \cdot \frac{12}{3 x - 6}$

Step 1

Factor $5$ out of $5 x - 10$ .

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Step 1.1

Factor $5$ out of $5 x$ .

$\frac{5 (x) - 10}{6} \cdot \frac{12}{3 x - 6}$

Step 1.2

Factor $5$ out of $- 10$ .

$\frac{5 x + 5 \cdot - 2}{6} \cdot \frac{12}{3 x - 6}$

Step 1.3

Factor $5$ out of $5 x + 5 \cdot - 2$ .

$\frac{5 (x - 2)}{6} \cdot \frac{12}{3 x - 6}$

Step 2

Factor $3$ out of $3 x - 6$ .

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Step 2.1

Factor $3$ out of $3 x$ .

$\frac{5 (x - 2)}{6} \cdot \frac{12}{3 (x) - 6}$

Step 2.2

Factor $3$ out of $- 6$ .

$\frac{5 (x - 2)}{6} \cdot \frac{12}{3 x + 3 \cdot - 2}$

Step 2.3

Factor $3$ out of $3 x + 3 \cdot - 2$ .

$\frac{5 (x - 2)}{6} \cdot \frac{12}{3 (x - 2)}$

Step 3

Cancel the common factor of $x - 2$ .

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Step 3.1

Factor $x - 2$ out of $5 (x - 2)$ .

$\frac{(x - 2) \cdot 5}{6} \cdot \frac{12}{3 (x - 2)}$

Step 3.2

Factor $x - 2$ out of $3 (x - 2)$ .

$\frac{(x - 2) \cdot 5}{6} \cdot \frac{12}{(x - 2) \cdot 3}$

Step 3.3

Cancel the common factor.

$\frac{(x - 2) \cdot 5}{6} \cdot \frac{12}{(x - 2) \cdot 3}$

Step 3.4

Rewrite the expression.

$\frac{5}{6} \cdot \frac{12}{3}$

Step 4

Cancel the common factor of $6$ .

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Step 4.1

Factor $6$ out of $12$ .

$\frac{5}{6} \cdot \frac{6 (2)}{3}$

Step 4.2

Cancel the common factor.

$\frac{5}{6} \cdot \frac{6 \cdot 2}{3}$

Step 4.3

Rewrite the expression.

$5 \cdot \frac{2}{3}$

Step 5

Combine $5$ and $\frac{2}{3}$ .

$\frac{5 \cdot 2}{3}$

Step 6

Multiply $5$ by $2$ .

$\frac{10}{3}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{10}{3}$

Decimal Form:

$3.\overline{3}$

Mixed Number Form:

$3 \frac{1}{3}$