Final answer:
The division of (2x-12)/3 by (4x-24)/7 simplifies to 7/6 or 1 1/6 after multiplying by the reciprocal, cancelling common factors, and multiplying the resulting fractions.
Step-by-step explanation:
The question at hand is a division of rational expressions. To simplify the expression (2x-12)/(3) ÷ (4x-24)/(7), we should first understand that dividing by a fraction is the same as multiplying by its reciprocal. Therefore, we invert the second fraction and multiply.
(2x-12)/3 × 7/(4x-24)
Next, we look for ways to simplify the expression before multiplying. We factor out a common factor of 2 from the numerators:
(2(x-6))/3 × 7/(2(2x-12))
Now, we simplify the fractions by reducing common factors:
(x-6)/3 × 7/(2x-12)
Given that 2x-12 can be factored further to 2(x-6), we can simplify further:
(x-6)/3 × 7/2(x-6)
We can now cancel out the (x-6) terms:
1/3 × 7/2
The final step is to multiply the resulting fractions:
(1 × 7) / (3 × 2) = 7/6 or 11/6
Therefore, the simplified expression is 7/6 or 11/6.