Question

What’s the domain of f(x)= x-4/x^2+5x-36

Answer 1

`f(x)=(x-4)/(x^2+5x-36)\\\\The\ domain:\\\\x^2+5x-36\\eq0\\\\x^2+9x-4x-36\\eq0\\\\x(x+9)-4(x+9)\\eq0\\\\(x+9)(x-4)\\eq0\iff x+9\\eq0\ \wedge\ x-4\\eq0\\\\x\\eq-9\ \wedge\ x\\eq4\\\\Answer:\ x\in\mathbb{R}-\{-9,\ 4\}\to x\in(-\infty,\ -9)\ \cup\ (-9,\ 4)\ \cup\ (4,\ \infty)\\\\\to x\\eq-9\ \wedge\ x\\eq4`