If `((a)/(b))^(x - 1) = ((b)/(a))^(x - 3)` , find the value x .

If (a/b)^(x-1) = (b/a)^(2x-8) , then find the value of x.

If (x+5)/((x-1)^(2))=(A)/((x-1))+(B)/((x-1)^(2)) , then find the values of A and B .

If the range of the function f(x)= cot^(-1)((x^(2))/(x^(2)+1)) is (a, b), find the value of ((b)/(a)+2) .

If abx^(2)=(a-b)^(2)(x+1) , then find the value of 1+(4)/(x)+(4)/(x^(2)) in terms of a and b.

The LCM of the polynomials (x^(2) + x - 2) (x^(2) + x -a) and (x^(2) + x -b) (x^(2) + 5x + a) " is " (x -1) (x +2) (x +3) , then find the values of a and b

If lim_(xto0) ((4x-1)^(1/3)+a+bx)/(x)=1/3 then find the values of a and b.