1
2/[3(x+2)]+(x²-x-3)/[(x-2)(x+2)]-1=(2x-4+3x²-3x-9-3x²+12)/[3(x²-4)]=
=-(x+1)/(3x²-12)
2
1+(2a+1)/[(a-1)(a²+a+1)]-a/(a-1)=(a³-1+2a+1-a³-a²-a)/(a³-1)=
=(-a²+a)/(a³-1)=-a(a-1)/[(a-1)(a²+a+1)]=-a/(a²+a+1)
3
a-(a³-15a-4)/(a²-16)=(a³-16a-a³+15a+4)/(a²-16)=(4-a)/[(a-4)(a+4)]=-1/(a+4)
4
(b²-16b+12)/[(b+2)(b²-2b+4)]+(3b+2)/(b²-2b+4)-3/(b+2)=
=(b²-16b+12+3b²+6b+2b+4-3b²+6b-12)/(b³+8)=
=(b²-2b+4)/[(b+2)(b²-2b+4)]=1/(b-2)