If `(3x)/((x-2)(x+1))` = `(2)/(x-2)`+`(A)/(x+1)`.then find `A`

If cos^(-1).(6x)/(1 + 9x^(2)) = -(pi)/(2) + 2 tan^(-1) 3x , then find the values of x

If f:RtoR,f(x)=(sqrt(x^(2)+1)-3x)/(sqrt(x^(2)+1)+x) then find the range of f(x) .

"Let "f(x)=((2^(x)+2^(-x))sin x sqrt(tan^(-1)(x^(2)-x+1)))/((7x^(2)+3x+1)^(3)) . Then find the value of f'(0).

If 3x - (1)/(3x ) =5 , find : (i) 9x^(2) + (1)/( 9x^2)

Evaluate : (i) (3x + (1)/(2) ) (2x + (1)/(3) )

Check whether the following are quadratic equation (i) (x+1)^2=2(x-3) (ii) x^2-2x=(-2)(3-x) (iii) (x-2)(x+1)=(x-1)(x+3) (iv) (x-3)(2x+1)=x(x+5) (v) (2x-1)(x-3)=(x+5)(x-1) (vi) x^2+3x+1=(x-2)^2 (vii) (x+2)^3=2x(x^2-1) (viii) x^3-4x^2 – x + 1 = (x – 2)^3

If 3x + (1)/(3x) = 3 , find : (i) 9x^(2) + (1)/(9x^2)

If f(x) = (3x-2)/(2x-3),AA x in R -{(3)/(2)} , " Find " f^(-1)

If (x^(2) + 1)/(x)= 3(1)/(3) and x gt 1 , find x- (1)/(x)

If (x^(2) + 1)/(x)= 3(1)/(3) and x gt 1 , find x^(3)- (1)/(x^(3))