1/(x-1)-1/(x+1)-2/(x^2 +1)+4/(x^4 +1)
=[(x+1)-(x-1)]/(x2-1)-2/(x^2 +1)+4/(x^4 +1)
=2/(x2-1)-2/(x^2 +1)+4/(x^4 +1)
=[2(x^2+1)-2(x^2-1)]/(x^4-1)+4/(x^4 +1)
=4/(x^4-1)+4/(x^4 +1)
=[4(x^4+1)+4(x^4-1)]/(x^8-1)
=8x^4/(x^8-1)
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1/(x-1)-1/(x+1)-2/(x^2 +1)+4/(x^4 +1)
=[(x+1)-(x-1)]/(x2-1)-2/(x^2 +1)+4/(x^4 +1)
=2/(x2-1)-2/(x^2 +1)+4/(x^4 +1)
=[2(x^2+1)-2(x^2-1)]/(x^4-1)+4/(x^4 +1)
=4/(x^4-1)+4/(x^4 +1)
=[4(x^4+1)+4(x^4-1)]/(x^8-1)
=8x^4/(x^8-1)