Simplify ((3x-6)/(3x-9))÷((4x-8)/(x-3))

$\frac{3 x - 6}{3 x - 9} \div \frac{4 x - 8}{x - 3}$

To divide by a fraction, multiply by its reciprocal.

$\frac{3 x - 6}{3 x - 9} \cdot \frac{x - 3}{4 x - 8}$

Cancel the common factor of $3 x - 6$ and $3 x - 9$ .

Factor $3$ out of $3 x$ .

$\frac{3 (x) - 6}{3 x - 9} \cdot \frac{x - 3}{4 x - 8}$

Factor $3$ out of $- 6$ .

$\frac{3 (x) + 3 \cdot - 2}{3 x - 9} \cdot \frac{x - 3}{4 x - 8}$

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

$\frac{3 (x - 2)}{3 x - 9} \cdot \frac{x - 3}{4 x - 8}$

Cancel the common factors.

Factor $3$ out of $3 x$ .

$\frac{3 (x - 2)}{3 (x) - 9} \cdot \frac{x - 3}{4 x - 8}$

Factor $3$ out of $- 9$ .

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

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

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

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $x - 3$ .

Cancel the common factor.

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

Rewrite the expression.

$(x - 2) \frac{1}{4 x - 8}$

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

Factor $4$ out of $4 x$ .

$(x - 2) \frac{1}{4 (x) - 8}$

Factor $4$ out of $- 8$ .

$(x - 2) \frac{1}{4 x + 4 \cdot - 2}$

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

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

Cancel the common factor of $x - 2$ .

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

$(x - 2) \frac{1}{(x - 2) \cdot 4}$

Cancel the common factor.

$(x - 2) \frac{1}{(x - 2) \cdot 4}$

Rewrite the expression.

$\frac{1}{4}$

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{4}$

Decimal Form:

$0.25$