Question

(x-1)^2(x+1)^3/x^4(x-2) is less than or equal to 0

Answer 1

$\dfrac{ {(x - 1)}^{2} {(x + 1)}^{3} }{ {x}^{4}(x - 2) \: } \: \leqslant 0 \:$

Alternate form -

$\dfrac{ {(x - 1)}^{2} {(x + 1)} }{ {x}^{2}(x - 2) \: } \: \leqslant 0 \:$


Critical points : -1 , 0 , 1 , 2 ( x ≠ 0 ; x ≠ 2 )

Solutions :-
[ -1 , 0 ) and ( 0 , 2 )

Integral solutions :- { -1 } and { 1 }