At which values of [[$ x $]] is the rational expression defined?

a) [[$ \displaystyle\frac {2x^2 + x + 3} {x - 5} $]]

Answer: The rational expression is defined when [[$ x $]] ≠ .

b) [[$ \displaystyle\frac {12- x} {\sqrt {(x - 1)^2}} $]]

Answer: The rational expression is defined when [[$ x $]] ≠ .

c) [[$ \displaystyle\frac {4x} {|2x - 2|} $]]

Answer: The rational expression is defined when [[$ x $]] ≠ .

d) [[$ \displaystyle\frac {5} {2x - 8} $]]

Answer: The rational expression is defined when [[$ x $]] ≠ .