" 2.Prove that "(1)/(1+x^(a-b))+(1)/(1+y^(b-a))=1

Prove that: (1)/(1+x^(a-b))+(1)/(1+x^(b-a))=1

Prove that: 1/(1+x^(a-b))+1/(1+x^(b-a))=1

Prove that (i) (a^(-1))/(a^(-1) + b^(-1)) + (a^(-1))/(a^(-1)-b^(-1)) = (2b^(2))/(b^(2) -a^(2)) (ii) (1)/(1+x^(a-b)) + (1)/(1+x^(b-a)) = 1

If the lines ax+y+1=0,x+by+1=0 and x+y+c=0 are concurrent (a!=b!=c!=1), prove that (1)/(1-a)+(1)/(1-b)+(1)/(1-c)=1

If x,y,z are not all zero such that ax+y+z=0,x+by+z=0x+y+cz=0 then prove that (1)/(1-a)+(1)/(1-b)+(1)/(1-c)=1

Prove that: (a^(-1)+b^(-1))^(-1)=(a b)/(a+b)

Prove that: 1/(1+x^(b-a)+\ x^(c-a))+1/(1+x^(a-b)+\ x^(c-b))+1/(1+x^(b-c)+x^(a-c))=1

a^(x)=b^(y)=c^(z) and b^(2)=ac then prove that (1)/(x)+(1)/(z)=(2)/(y)

Prove that: :(a^(-1)+b^(-1))^(-1)=(ab)/(a+b)