[latex] \frac{a}{a^2-1}+ \frac{a^2+a-1}{a^3-a^2+a-1}+ \frac{a^2-a-1}{a^3+a^2+a+1}- \frac{2a^3}{a^4-1} [/latex]= [latex](1- \frac{a^-^n+b^-^n}{a^-^n-b^-^n})^-^2[/latex]=

1 a/(a-1)(a+1)+(a²+a-1)/(a-1)(a²+1)+(a²-a-1)/((a+1)(a²+1)-2a³/(a²-1)(a²-1)= =[a(a²+1)+(a+1)(a²+a-1)+(a-1)(a²-a-1)-2a³]/(a²-1)(a²+1)= =(a³+a+a³+a²-a+a²+a-1+a³-a²-a-a²+a+1-2a³)/(a²-1)(a²+1)=0/(a²-1)(a²+1)=0 2 a^-n+b^-n=1/a^n+1/b^n=(b^n+a^n)/(ab)^n a^-n-b^-n=1/a^n-1/b^n=(b^n-a^n)/(ab)^n (b^n+a^n)/(ab)^n :(b^n-a^n)/(ab)^n=(b^n+a^n)/(b^n-a^n) 1-(b^n+a^n)/(b^n-a^n)=(b^n-a^n-b^n-a^n)/(b^n-a^n)=-2a^n/(b^n-a^n) [-2a^n/(b^n-a^n)]^-2=(b^n-a^n)²/4a^2n