Divide. (6x-12)/(21x-14)div (2x-4)/(3x-2) Simplify your answer as much as possible. square

To divide the given rational expressions, we multiply the first expression by the reciprocal of the second expression. <br /><br />Given: <br />$$\frac {6x-12}{21x-14}\div \frac {2x-4}{3x-2}$$<br /><br />Step 1: Find the reciprocal of the second fraction.<br />Reciprocal of $\frac {2x-4}{3x-2}$ is $\frac {3x-2}{2x-4}$.<br /><br />Step 2: Multiply the first fraction by the reciprocal of the second fraction.<br />$$\frac {6x-12}{21x-14} \times \frac {3x-2}{2x-4}$$<br /><br />Step 3: Simplify the expression.<br />$$\frac {(6x-12)(3x-2)}{(21x-14)(2x-4)}$$<br /><br />Step 4: Factor out common terms in the numerator and denominator.<br />$$\frac {6(3x-2)}{21(2x-4)}$$<br /><br />Step 5: Simplify further.<br />$$\frac {18x-12}{42x-28}$$<br /><br />Step 6: Simplify the fraction.<br />$$\frac {18x-12}{42x-28} = \frac {3(6x-2)}{7(6x-2)}$$<br /><br />Step 7: Cancel out common terms.<br />$$\frac {3}{7}$$<br /><br />Therefore, the simplified expression is $\frac {3}{7}$.