`if (x+2)/(x-2) =2/3 ,then x = `

If f(x+2)=(x+3)^(2)-2x , then f(x)=

IF ax^3+bx^2+cx+d = |(x^2,(x-1)^2, (x-2)^2) ,((x-1)^2, (x-2)^2, (x-3)^2), ((x-2)^2, (x-3)^2, (x-4)^2)| , then d= (A) 1 (B) -8 (C) 0 (D) none of these

Solve for x : 1/ ((x -1)(x -2))+1/( (x-2)(x-3))=2/ 3', x is not equal to 1,2,3 .

Find the greatest and least values of (x+2)/(2x^(2)+3x+6) AA x in R

If the roots x_(1),x_(2),x_(3) of the equation x^(3)+ax+a=0 (where a in R-{0} ) satisfy (x_(1)^(2))/(x_(2))+(x_(2)^(2))/(x_(3))+(x_(3)^(2))/(x_(1))=-8 , then find the value of a and the roots of the given cubic equation.

If (x^(2)+1)/((x^(2)+2)(x^(2)+3))=(A)/(x^(2)+3)+(B)/(x^(2)+2) then (A, B)=

If (3x+2)/((x+1)(2x^(2)+3))=(A)/(x+1)-(Bx+C)/(2x^(2)+3) , then A+B-C=

If (x ^(2) +x+1) + (x^(2) + 2x +3) + (x^(2) + 3x +5) + ….. + (x ^(2) + 20x + 39) =4500, then x is equal to :

Foctorise : x^(2) +(1)/(x^(2)) - 2 -3 x+ (3)/(x)

If f(x)+2f(1-x)=x^2+2AAx in Rt h e nf(x) is given by ((x-2)^2)/3 2. x^2-2 3. (x-2)^2 4. (x^2-2)/3 (x^2)/3-2