Explanation:
The area of the trapezoid is the average of the bases times the height
[ (k+3)/3 + (3k+1)/3 ] /2 * 1/(k^2-1) <====now simplify with several steps:
=
(4k+4)/6 * 1 /(k^2-1)
(2k+2)/3 * 1 /(k^2-1)
(2k+2)/(3 (k^2-1) )
2(k+1)/[3 (k+1)(k-1)]
2 / (3(k-1))