We rewrite the equation as
1-1/(x-2)^2>=0
We do some simplifications
((x-2)^2-1)/(x-2)^2>=0
((x-2-1)(x-2+1))/(x-2)^2>=0
((x-3)(x-1))/(x-2)^2>=0
Let f(x)=((x-3)(x-1))/(x-2)^2
The domain of f(x) is D_f(x)=RR-{2}
The denominator is >0, AA x in D_f(x)
We can do the sign chart
color(white)(aaaa)xcolor(white)(aaaa)-oocolor(white)(aaaa)1color(white)(aaaa)2color(white)(aaaa)3color(white)(aaaa)+oo
color(white)(aaaa)x-1color(white)(aaaa)-color(white)(aaaa)+∣∣color(white)(aa)+color(white)(aaa)+
color(white)(aaaa)x-3color(white)(aaaa)-color(white)(aaaa)-∣∣color(white)(aa)-color(white)(aaa)+
color(white)(aaaa)f(x)color(white)(aaaa)+color(white)(aaaaa)-∣∣color(white)(aa)-color(white)(aaaa)+
Therefore,
f(x)>=0, when x in ] -oo,1 ] uu [3, +oo[
graph{(y-((x-1)(x-3))/(x-2)^2)=0 [-8.89, 8.89, -4.444, 4.445]}
