(4a)/(a^2-1)+(1+a)/(1-a)
=(4a)/(a^2-1)-(1+a)^2/[(a-1)(a+1)]
=(4a)/(a^2-1)-(1+a)^2/(a^2-1)
=[4a-(a^2+2a+1)]/(a^2-1)
=-(a^2-2a+1)/(a^2-1)
=-(a-1)^2/[(a-1)(a+1)]
=(1-a)/(a+1)