Question

What is the product? StartFraction 4 k + 2 Over k squared minus 4 EndFraction times StartFraction k minus 2 Over 2 k + 1 EndFraction StartFraction 4 Over 2 k + 1 EndFraction StartFraction 2 Over k minus 2 EndFraction StartFraction 2 Over 2 k + 1 EndFraction StartFraction 2 Over k + 2 EndFraction

Answer 1

d. StartFraction 2 Over k + 2 EndFraction

aka

d. 2/k+2

Answer 2

`(2)/(k+2)`

Explanation:

Given the expression:

`(4k+2)/(k^2-4) * (k-2)/(2k+1)`

We are to find the product as shown:

`= (4k+2)/(k^2-4) * (k-2)/(2k+1)\\\\= (2(2k+1))/(k^2-2^2) * (k-2)/(2k+1)\\\\= (2(2k+1))/((k-2)(k+2)) * (k-2)/(2k+1)\\\\= (2)/(k+2) * 1\\\\= (2)/(k+2)`

Hence the required function is
`(2)/(k+2)`