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

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

(1/x-1)-(1/x+1)-(2/x^2+1)-(4/x^4+1)-(8/x^8+1)
1/(x-1)-1/(x+1)-2/(x^2+1)-4/(x^4+1)-8/(x^8+1)
=(x+1)/(x+1)(x-1)-(x-1)/(x+1)(x-1)-2/(x^2+1)-4/(x^4+1)-8/(x^8+1)
=[(x+1)-(x-1)]/(x^2-1)-2/(x^2+1)-4/(x^4+1)-8/(x^8+1)
=2/(x^2-1)-2/(x^2+1)-4/(x^4+1)-8/(x^8+1)
=2(x^2+1)/(x^2+1)(x^2-1)-2(x^2-1)/(x^2+1)(x^2-1)-4/(x^4+1)-8/(x^8+1)
=[2(x^2+1)-2(x^2-1)]/(x^4-1)-4/(x^4+1)-8/(x^8+1)
=4/(x^4-1)-4/(x^4+1)-8/(x^8+1)
=4(x^4+1)/(x^4+1)(x^4-1)-4(x^4-1)/(x^4+1)(x^4-1)-8/(x^8+1)
=[4(x^4+1)-4(x^4-1)]/(x^8-1)-8/(x^8+1)
=8/(x^8-1)-8/(x^8+1)
=8(x^8+1) /(x^8+1) (x^8-1)-8(x^8-1)/(x^8+1) (x^8-1)
=[8(x^8+1) -8(x^8-1)]/(x^16-1)
=16/(x^16-1)


(1/x-1)-(1/x+1)-(2/x^2+1)-(4/x^4+1)-(8/x^8+1)
=[(x+1)-(x-1)]/[x^2-1]-(2/x^2+1)-(4/x^4+1)-(8/x^8+1)
=2/[x^2-1]-(2/x^2+1)-(4/x^4+1)-(8/x^8+1)
=4/(x^4-1)-(4/x^4+1)-(8/x^8+1)
=8/(x^8-1)-8/(x^8+1)
=16/(x^16-1)

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