Final answer:
The expression equivalent to ((6c² + 3c)/(-4x + 2))/((2c + 1)/(4c-2)) is 3c(2c - 1)/(-4x + 2).
Step-by-step explanation:
To find the expression that is equivalent to ((6c² + 3c)/(-4x + 2))/((2c + 1)/(4c-2)), we can simplify each part separately. First, simplify the numerator of the fraction: (6c² + 3c). This can be factored as 3c(2c + 1). Then, simplify the denominator of the fraction: (-4x + 2). This can be factored as 2(-2x + 1). Next, simplify the numerator of the second fraction: (2c + 1). And finally, simplify the denominator of the second fraction: (4c - 2). This can be factored as 2(2c - 1). Now, we can rewrite the original expression as (3c(2c + 1))/(2(-2x + 1)) ÷ ((2c + 1)/(2(2c - 1))). To divide by a fraction, we can multiply by its reciprocal. So, multiplying the numerator and denominator by (2(2c - 1))/(2c + 1), we get (3c(2c + 1))/(2(-2x + 1)) * (2(2c - 1))/(2c + 1). We can cancel out common factors, which gives us the simplified expression: 3c(2c - 1)/(-4x + 2).