For the function y=x/(2x^2-3x-2), how to tell what is the domain of function?

We'll recall the definition of the domain of the function.
The domain of the function comprises all the values of variable x that makes the
expression of the function to exist.

In this case, the
expression of the function is a fraction. The important condition for a fraction to be
possible is that the denominator not to be zero
value.

We'll check what are the x values that cancel the
denominator. Simce the denominator is a quadratic, we'll apply quadratic
formula:

x1 =
[3+sqrt(9+16)]/4

x1 =
(3+5)/4

x1 = 2

x2 =
(3-5)/4

x2 =
-1/2

The domain of definition of the given
function is the real numbers set, except the values {-1/2 ; 2}, that cancel the
denominator.