Simplify ((4-6x)/24)÷((2-3x)/8)

$\frac{4 - 6 x}{24} \div \frac{2 - 3 x}{8}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{4 - 6 x}{24} \cdot \frac{8}{2 - 3 x}$

Step 2

Cancel the common factor of $8$ .

Factor $8$ out of $24$ .

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

Cancel the common factor.

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

Rewrite the expression.

$\frac{4 - 6 x}{3} \cdot \frac{1}{2 - 3 x}$

Step 3

Multiply $\frac{4 - 6 x}{3}$ by $\frac{1}{2 - 3 x}$ .

$\frac{4 - 6 x}{3 (2 - 3 x)}$

Step 4

Factor $2$ out of $4 - 6 x$ .

Factor $2$ out of $4$ .

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

Factor $2$ out of $- 6 x$ .

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

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

$\frac{2 (2 - 3 x)}{3 (2 - 3 x)}$

Step 5

Cancel the common factor of $2 - 3 x$ .

Cancel the common factor.

$\frac{2 (2 - 3 x)}{3 (2 - 3 x)}$

Rewrite the expression.

$\frac{2}{3}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{2}{3}$

Decimal Form:

$0.\overline{6}$