Simplify ((x-2)/(3x))÷((4x-8)/(6x))

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

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 $3 x$ .

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

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 3

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

Factor $4$ out of $4 x$ .

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

Factor $4$ out of $- 8$ .

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

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

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

Step 4

Cancel the common factor of $x - 2$ .

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

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

Cancel the common factor.

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

Rewrite the expression.

$\frac{2}{4}$

Step 5

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

Factor $2$ out of $2$ .

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

Cancel the common factors.

Factor $2$ out of $4$ .

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

Cancel the common factor.

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

Rewrite the expression.

$\frac{1}{2}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{2}$

Decimal Form:

$0.5$