Algebra Examples

$\frac{x - 5}{6} \div \frac{2 x - 10}{12}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{x - 5}{6} \cdot \frac{12}{2 x - 10}$

Step 2

Cancel the common factor of $6$ .

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Step 2.1

Factor $6$ out of $12$ .

$\frac{x - 5}{6} \cdot \frac{6 (2)}{2 x - 10}$

Step 2.2

Cancel the common factor.

$\frac{x - 5}{6} \cdot \frac{6 \cdot 2}{2 x - 10}$

Step 2.3

Rewrite the expression.

$(x - 5) \frac{2}{2 x - 10}$

Step 3

Factor $2$ out of $2 x - 10$ .

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Step 3.1

Factor $2$ out of $2 x$ .

$(x - 5) \frac{2}{2 (x) - 10}$

Step 3.2

Factor $2$ out of $- 10$ .

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

Step 3.3

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

$(x - 5) \frac{2}{2 (x - 5)}$

Step 4

Cancel the common factor of $x - 5$ .

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Step 4.1

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

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

Step 4.2

Cancel the common factor.

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

Step 4.3

Rewrite the expression.

$\frac{2}{2}$

Step 5

Divide $2$ by $2$ .

$1$