Question

Solve the following inequality:
$(x^2-2x)(2x-2)-9\frac{2x-2}{x^2-2x}⩽0$

Answer 1

$(x^2-2x)(2x-2)-9\frac{2x-2}{x^2-2x}\le 0$

$(2x-2)\frac{\left(\right(x^2-2x{)}^2-3^2)}{x(x-2)}\le 0$

$\frac{(x-1)(x^2-2x-3)\left(\right(x-1{)}^2+2)}{x(x-2)}\le 0$

$(x+1)x(x-1)(x-2)(x-3)\le 0$

$⟹x\in (-\infty ,-1]\cup [0,1]\cup [2,3]$