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