Question

What expression is equivalent to x-5/(x-5)(x-4)

Answer 1

Answer:

$\large\boxed{\dfrac{1}{x-4}\ \text{for}\ x\neq5\ \wedge\ x\neq4}$

Step-by-step explanation:

$\dfrac{x-5}{(x-5)(x-4)}\\\\\text{Domain:}\ (x-5\neq0\ \wedge\ x-4\neq0)\Rightarrow(x\neq5\ \wedge\ x\neq4)\\\\\dfrac{x-5}{(x-5)(x-4)}\qquad\text{cancel}\ (x-5)\\\\=\dfrac{1}{x-4}$