You should rename main variable (especially if you are beginner) in some simple letter, eg $x$. Function definition should start from f[x_]:= (*something with x as independent variable*)

So main definition is:

f[x_] := (-2 a (-2 + b)^2 (1 + b) c +  c^2 (2 b^3 + 8 x - 6 b^2 x))/(2 (-4 + b^2)^2);

Plot works well:

Plot[f[x], {x, 1, 9}, PlotRange -> All, Frame -> True, 
 FrameLabel -> {"x", "f(x)"}, 
 LabelStyle -> {FontFamily -> "Arial", FontSize -> 12}]

so other operations with f[x] should be OK.

Thank you so much!!! It was incredibly helpful and I really appreciated it. Thank you so much again. Have a wonderful day

Sincerely Jee young