Question

Solve inequality:

$\frac{(x+2)(x^2-2x+1)}{4+3x-x^2}\ge O$

Answer 1

$\frac{(x+2)(x^2-2x+1)}{(4+3x-x^2)}\ge 0$

or, $\frac{(x+2){(x-1)}^2}{4+4x-x-x^2}\ge 0$

or, $\frac{(x+2){(x-1)}^2}{4(1+x)-x(1+x)}\ge 0$

or, $\frac{(x+2){(x-1)}^2(4-x)(1+x)}{{(4-x)}^2{(1+x)}^2}\ge 0$

or, $(x+2){(x-1)}^2(4-x)(1+x)\ge 0$

[$\therefore$ Square of any quantity is greates than $0$]

or, $a\ge -2,a\le 1,a\le 4,a\ge -1$