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

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

If y=1+(1)/(x-1)+(2x)/((x-1)(x-2))+(3x^(2))/((x-1)(x-2)(x-3)) , then the value of -9y'(4) is equal to

(x^(2)+x+1)/((x-1)(x-2)(x-3))=A/(x-1)+B/(x-2)+C/(x-3) rArr A+C=

If the interval of differencing is unity prove that Delta[x(x+1)(x+2)(x+3)]=4(x+1)(x+2)(x+3)

Find derivatives of the following function. ((x+1)(x+2)^2(x+3)^3)/((x-1)(x-2)^2(x-3)^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 ]]

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 ]]

Evaluate (x + 2)/((x + 1)(2x+ 3)) - (2x + 3)/((x + 1)(x + 2)) + (3x + 5)/((2x + 3)(x + 2))