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`

Answer

`(i) (-3,-2) uu (1,3)` `(ii) {-2}uu[1,8)` `(iii)(-2,(3-sqrt(5))/(2)]uu(1,(3+sqrt(5))/(2)]`
`(iv) (-oo,1)-{0}` `(v) (-3,-2) uu (-1,oo)` `(vi) [1,6]`