Simpify : `(1)/((4x^3-3x)^2)-{((3sqrt(1-x^2))/(x)-((1-x^2)^(3/2))/(x^3))/(1-3((1-x^2)/(x^2)))}^2`.

Let tan^(-1)y=tan^(-1)x+tan^(-1)((2x)/(1-x^2)) , where |x|<1/(sqrt(3)) . Then a value of y is : (1) (3x-x^3)/(1-3x^2) (2) (3x+x^3)/(1-3x^2) (3) (3x-x^3)/(1+3x^2) (4) (3x+x^3)/(1+3x^2)

Let tan^(-1)y=tan^(-1)x+tan^(-1)((2x)/(1-x^2)) , where |x|<1/(sqrt(3)) . Then a value of y is : (1) (3x-x^3)/(1-3x^2) (2) (3x+x^3)/(1-3x^2) (3) (3x-x^3)/(1+3x^2) (4) (3x+x^3)/(1+3x^2)

Let tan^(-1)y=tan^(-1)x+tan^(-1)((2x)/(1-x^(2))) where |x|<(1)/(sqrt(3))* Then a value of y is : (1)(3x-x^(3))/(1-3x^(2))(2)(3x+x^(3))/(1-3x^(2))(3)(3x-x^(3))/(1+3x^(2))(4)(3x+x^(3))/(1+3x^(2))

Let tan^(-1)y=tan^(-1)x+tan^(-1)((2x)/(1-x^2)) , where |x|<1/(sqrt(3)) . Then a value of y is : (1) (3x-x^3)/(1-3x^2) (2) (3x+x^3)/(1-3x^2) (3) (3x-x^3)/(1+3x^2) (4) (3x+x^3)/(1+3x^2)

Expand (2x^(2)-3sqrt(1-x^(2)))^(4)+(2x^(2)+3sqrt(1-x^(2)))^(4)

lim_(x to oo ) (sqrt(3x^(2)-1)-sqrt(2x^(2)-3))/(4x+3)

lim_(x to oo ) (sqrt(3x^(2)-1)-sqrt(2x^(2)-3))/(4x+3)