Answer:
[tex]\large\boxed{\dfrac{1}{x-4}\ \text{for}\ x\neq5\ \wedge\ x\neq4}[/tex]
Step-by-step explanation:
[tex]\dfrac{x-5}{(x-5)(x-4)}\\\\\text{Domain:}\ (x-5\neq0\ \wedge\ x-4\neq0)\Rightarrow(x\neq5\ \wedge\ x\neq4)\\\\\dfrac{x-5}{(x-5)(x-4)}\qquad\text{cancel}\ (x-5)\\\\=\dfrac{1}{x-4}[/tex]
