If `x^2/(x-2) gt 0`, then `x in...`

If (|x-1|)/(x-2)gt0 , then:

Fill in the blanks of the following (i) If -4x ge 12," then "x…-3 . (ii) If (-3)/4 x le -3," then "x…4 . (iii) If 2/(x+2) gt 0,"then " x…-2 . (iv) If x gt -5," then "4x…-20 . (v) If x gt y and z lt 0," then "-xz…-yz . ( vi) If p gt 0 and q lt 0," then "p-q...p . (vii) If |x+2| gt 5," then "x...-7 or x...3 . (viii) If -2x+1 ge 9," then "x...-4 .

Solve x^2-x-2 gt 0.

Solve x^(2)-x-2 gt 0 .

Given the function f(x) = x^(2) e^(-2x), x gt 0 . Then f(x) has the maximum value equal to

If (x-3)/(2) gt 0 then the value of x is ________.

If 496 xx 492 = x^(2) - 4 (x gt 0) , then x = "________" .

If x is an integer satisfying x^(2)-6x+5 le 0 " and " x^(2)-2x gt 0 , then the number of possible values of x, is