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