Corrections:

#1  a(a-1)/[(a+1)(a+2)(a+3)]  *  (a+1)(a+2)/[5a(a-1)] = 1/(5a+15)

#8  2x^2 -15x -8 = 0   factors to (2x-1)(x-8)=0 so x= 1/2 or 8  !