Rayon fabrics make wonderfully comfortable clothing, but require some TLC when sewing.  Because rayons will fray easily, the raw edges need careful treatment.  I recommend serging all exposed raw edges before assembling a garment made with rayon.  If this is not possible, then cut the pieces out with pinking shears AND zig-zag finish all exposed raw edges.  Use a "triple" zig-zag if your machine has one - this is a series of 3 small stitches in each direction.