Rule: You cannot divide by zero.
Since zero cannot be in the denominator, the 2x-9 must be nonzero.
If it was zero, then...
2x-9 = 0
2x = 9
x = 9/2
x = 4.5
If x = 4.5, then the denominator is zero and causes a division by zero error.
We must kick this x value out of the domain. Poke a hole on the real number line at x = 4.5
We'll go from [tex](-\infty, \infty)[/tex] to [tex](-\infty, 4.5) \cup (4.5, \infty)[/tex]