[" 4.Prove that: "],[qquad (" i) "(1)/(1+x^(a-b))+(1)/(1+x^(b-a))=1]

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

Show 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: 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

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

Prove that: x^4+4=(x+1+i)(x+1-i)(x-1+i)(x-1-i) .

Prove that. (i) sqrt(x^(-1) y) .sqrt(y^(-1) z) . Sqrt(z^(-1) x) = 1 (ii) ((1)/(x^(a-b)))^((1)/(a-c)).((1)/(x^(b-c))).((1)/(x^(c-b)))^((1)/(c-b))= 1 (iii) (x^(a(b-c)))/(x^(b(a-c))) div ((x^(b))/(x^(a))) (iv) ((x^(a+b))^(2)(x^(b+c))^(2)(x^(c+a))^(2))/((x^(a)x^(b)x^(c))^(4))