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

Compute:
(4k+2)/(k^2−4) * (k−2)/(2k+1).

Factor: 4k+2 = 2(2k+1), k^2−4 = (k−2)(k+2). So
= [2(2k+1)]/[(k−2)(k+2)] * (k−2)/(2k+1)
Cancel (2k+1) and (k−2):
= 2/(k+2).

Domain restrictions from the original expression: k ≠ 2, −2, −1/2.