Algebra Examples

$\frac{x - 2}{3 x} \div \frac{4 x - 8}{6 x}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{x - 2}{3 x} \cdot \frac{6 x}{4 x - 8}$

Step 2

Cancel the common factor of $3 x$ .

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Step 2.1

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

$\frac{x - 2}{3 x} \cdot \frac{3 x (2)}{4 x - 8}$

Step 2.2

Cancel the common factor.

$\frac{x - 2}{3 x} \cdot \frac{3 x \cdot 2}{4 x - 8}$

Step 2.3

Rewrite the expression.

$(x - 2) \frac{2}{4 x - 8}$

$(x - 2) \frac{2}{4 x - 8}$

Step 3

Factor $4$ out of $4 x - 8$ .

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Step 3.1

Factor $4$ out of $4 x$ .

$(x - 2) \frac{2}{4 (x) - 8}$

Step 3.2

Factor $4$ out of $- 8$ .

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

Step 3.3

Factor $4$ out of $4 x + 4 \cdot - 2$ .

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

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

Step 4

Cancel the common factor of $x - 2$ .

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Step 4.1

Factor $x - 2$ out of $4 (x - 2)$ .

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

Step 4.2

Cancel the common factor.

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

Step 4.3

Rewrite the expression.

$\frac{2}{4}$

$\frac{2}{4}$

Step 5

Cancel the common factor of $2$ and $4$ .

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Step 5.1

Factor $2$ out of $2$ .

$\frac{2 (1)}{4}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $2$ out of $4$ .

$\frac{2 \cdot 1}{2 \cdot 2}$

Step 5.2.2

Cancel the common factor.

$\frac{2 \cdot 1}{2 \cdot 2}$

Step 5.2.3

Rewrite the expression.

$\frac{1}{2}$

$\frac{1}{2}$

$\frac{1}{2}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{2}$

Decimal Form:

$0.5$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$