Final answer:
To divide (4c²-4c)/(9c-9) by (7)/(12c), we factor and simplify the expressions, then multiply by the reciprocal of the second term. After simplification and cross-cancelling, we get (16c²/21).
Step-by-step explanation:
To divide the given expressions (4c²-4c)/(9c-9) by (7)/(12c), we need to multiply the first expression by the reciprocal of the second. First, simplify the expressions where possible. The term (4c²-4c) can be factored to 4c(c-1) and (9c-9) to 9(c-1). The division sign is replaced by multiplication when taking the reciprocal of the second expression, giving us:
(4c(c-1)/9(c-1)) × (12c/7)
Cross cancel the (c-1) terms and any other common factors before multiplying. Now the equation looks like this:
(4c/9) × (12c/7)
Now multiply the numerators together and the denominators together:
(4c × 12c) / (9 × 7)
This simplifies to:
48c² / 63
The common factor of 3 in both numerator and denominator can be divided out, giving us:
(16c² / 21)