Simplify ((2x-9)/(3x))÷(4x-18)

$(\frac{2 x - 9}{3 x}) \div (4 x - 18)$

Step 1

Rewrite the division as a fraction.

$\frac{\frac{2 x - 9}{3 x}}{4 x - 18}$

Step 2

Multiply the numerator by the reciprocal of the denominator.

$\frac{2 x - 9}{3 x} \cdot \frac{1}{4 x - 18}$

Step 3

Factor $2$ out of $4 x - 18$ .

Factor $2$ out of $4 x$ .

$\frac{2 x - 9}{3 x} \cdot \frac{1}{2 (2 x) - 18}$

Factor $2$ out of $- 18$ .

$\frac{2 x - 9}{3 x} \cdot \frac{1}{2 (2 x) + 2 (- 9)}$

Factor $2$ out of $2 (2 x) + 2 (- 9)$ .

$\frac{2 x - 9}{3 x} \cdot \frac{1}{2 (2 x - 9)}$

Step 4

Cancel the common factor of $2 x - 9$ .

Factor $2 x - 9$ out of $2 (2 x - 9)$ .

$\frac{2 x - 9}{3 x} \cdot \frac{1}{(2 x - 9) \cdot 2}$

Cancel the common factor.

$\frac{2 x - 9}{3 x} \cdot \frac{1}{(2 x - 9) \cdot 2}$

Rewrite the expression.

$\frac{1}{3 x} \cdot \frac{1}{2}$

Step 5

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

$\frac{1}{3 x \cdot 2}$

Step 6

Multiply $2$ by $3$ .

$\frac{1}{6 x}$