(1)/(a+b+x)=(1)/(2)+(1)/(b)+(1)/(x)

(1)/(x+a)+(1)/(x+b)=(1)/(x+a+b)+(1)/(x)

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))

Let a,b,c be such that (1)/((1-x)(1-2x)(1-3x))=(a)/(1-x)+(b)/(1-2x)+(c)/(1-3x) then (a)/(1)+(b)/(3)+(c)/(5)

Let a, b, c such that (1)/((1-x)(1-2x)(1-3x))=(a)/(1-x)+(b)/(1-2x)+(c)/(1-3x), a/1+b/3+c/5=

Expression ((a+1/b)^(1/x)(a-1/b)^(1/x))/((b+1/a)^(1/x)(b-1/a)^(1/x)) is an integer if

If (2x-1)/((x+1)(x^(2)-1))=(A)/(x-1)+(B)/(x+1)+(C )/((x+1)^(2)) , then A , B , C , respectively are _______.

If (1)/((1+2x)(1-x^(2)))=(A)/(1+2x)+(B)/(1+x)+(C)/(1-x) then assending order of A, B, C.