Multiply. (k+3)/(4k-2)*(12k^2+2k-4)

a. 3(k+3)/3k+2
b. 3(k+3)(2k-1)/2
c. (k+3)(3k+2)***
d. (3k+1)(2k+3)

Please help? Thanks

factor the numberator:

(k+3)(3k+2)(4k-2)

which leaves after the deominator divides out, your answer.

To multiply the given expression (k+3)/(4k-2)*(12k^2+2k-4), we will use the distributive property of multiplication over addition or subtraction.

Step 1: Simplify the expression inside the parentheses.
12k^2 + 2k - 4 cannot be simplified further, so we leave it as it is.

Step 2: Apply the distributive property.
(k+3)/(4k-2)*(12k^2+2k-4) = (k+3)*(12k^2+2k-4)/(4k-2)

Step 3: Multiply each term of the numerator by the denominator.
= (k*12k^2 + k*2k + k*(-4) + 3*12k^2 + 3*2k - 3*4)/(4k-2)

Step 4: Simplify.
= (12k^3 + 2k^2 - 4k + 36k^2 + 6k - 12)/(4k-2)

Step 5: Combine like terms.
= (12k^3 + 38k^2 + 2k - 12)/(4k-2)

The correct option is (c) (k+3)(3k+2).