=(x+1)/(x^2-1)-(x-1)/(x^2-1)-2/(x^2+1)-4/(x^4+1)
=2/(x^2-1)-2/(x^2+1)-4/(x^4+1)
=2(x^2+1)/(x^4-1)-2(x^2-1)/(x^4-1)-4/(x^4+1)
=4/(x^4-1)-4/(x^4+1)
=8/(x^8-1)
=(x+1)/(x^2-1)-(x-1)/(x^2-1)-2/(x^2+1)-4/(x^4+1)
=2/(x^2-1)-2/(x^2+1)-4/(x^4+1)
=2(x^2+1)/(x^4-1)-2(x^2-1)/(x^4-1)-4/(x^4+1)
=4/(x^4-1)-4/(x^4+1)
=8/(x^8-1)