" (ii) "quad ((1-x)^(3)(x+2)^(4))/((x+9)^(2)(x-8))>=0

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

((2x-1)(x+3)(2-x)(1-x)^(2))/(x^(4)(x+6)(x-9)(2x^(2)+4x+9))<0

((x-4)^(2005)*(x+8)^(2008)(x+1))/(x^(2006)(x-2)^(3)*(x+3)^(5)0(x-6)(x+9)^(2010))<=0

Solve the following equations and also check your result in each case: (i) ((3x+1))/(16)+((2x-3))/7=((x+3))/8+((3x-1))/(14) (ii) ((1-2x))/7-((2-3x))/8=3/2+x/4 (iii) (9x+7)/2-\ (x-(x-2)/7)=36 (iv) 0. 18\ (5x-4)=\ 0. 5 x+0. 8

Solve the following equations and also check your result in each case: (i) ((3x+1))/(16)+((2x-3))/7=((x+3))/8+((3x-1))/(14) (ii) ((1-2x))/7-((2-3x))/8=3/2+x/4 (iii) (9x+7)/2-\ (x-(x-2)/7)=36 (iv) 0. 18\ (5x-4)=\ 0. 5 x+0. 8

The number of values of x for which sin^(-1)(x^(2)-(x^(4))/3+(x^(6))/9………)+cos^(-1)(x^(4)-(x^(8))/3+(x^(12))/9………)=(pi)/2 , where 0le|x|ltsqrt(3) , is

(x-4)^(3)+(x-9)^(3)+(x-8)^(3)=3(x-4)(x-9)(x-8), find the value of x.