((x-1)(x-2)(x-3))/((x+1)(x+2)(x+3))>1

Solve the following rational in equalities (i) ((x-1)(x+2))/((x-3)(x+3)) lt 0 (ii) ((1-x)^(3)(x+2)^(4))/((x+9)^(2)(x-8))ge0 (iii) ((x^(2)-3x+1)^(3))/((x-1)(x+2))le0 (iv) (x(2^(x)-3^(x)))/((x^(2)+x+1)(x-1))gt0 (v) ((x-1)(x-2)(x-3))/((x+1)(x+2)(x+3)) le1 (vi) 1 lt (3x^(2)-7x+8)/(x^(2)+1) le2

(x^(2)+5x+1)/((x+1)(x+2)(x+3))=(A)/(x+1)+(B)/((x+1)(x+2))+(C)/((x+1)(x+2)(x+3)) then B=

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

If D(x)=det[[(x-1),(x-1)^(2),x^(3)(x-1),x^(2),(x+1)^(3)x,(x+1)^(2),(x+1)^(3) then the coefficient of x in D(x), is ]]

Simplify and find the value of x: 1/((x-1)(x-2))+1/((x-2)(x-3))=2/3, x!= 1,2,3

If f(x)=det[[x-2,(x-1)^(2),x^(3)(x-1),x^(2),(x+1)^(3)x,(x+1)^(2),(x+2)^(3) then coefficient of x in f(x), is ]]

Check whether the following are quadratic equations : (1) (x-1)^(2)=2(x-3) (2) x^(2)-2x=(-2)(3-x) (3) (x-2)(x+1)=(x-1)(x+3) (4) (x-3)(2x+1)=x(x+5) (5) (2x-1)(x-3)=(x+5)(x-1) (6) x^(2)+3x+1=(x-2)^(2) (7) (x+2)^(3)=2x(x^(2)-1) (8) x^(3)-4x^(2)-x+1=(x-2)^(3)