Question

Find the domain of the ration function R(x)=7-2x/x^3-8x^2+7x

Answer 1

$R(x)=\dfrac{7-2x}{x^3-8x^2+7x}\\\\The\ domain:\\\\x^3-8x^2+7x\neq0\\\\x(x^2-8x+7)\neq0\\\\x(x^2-x-7x+7)\neq0\\\\x[x(x-1)-7(x-1)]\neq0\\\\x(x-1)(x-7)\neq0\iff x\neq0\ \wedge\ x-1\neq0\ \wedge\ x-7\neq0\\\\\boxed{x\neq0\ \wedge\ x\neq1\ \wedge\ x\neq7}\to\boxed{x\in\mathbb{R}-\{0,\ 1,\ 7\}}$