Question

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

Answer 1

`R(x)=(7-2x)/(x^3-8x^2+7x)\\\\The\ domain:\\\\x^3-8x^2+7x\\eq0\\\\x(x^2-8x+7)\\eq0\\\\x(x^2-x-7x+7)\\eq0\\\\x[x(x-1)-7(x-1)]\\eq0\\\\x(x-1)(x-7)\\eq0\iff x\\eq0\ \wedge\ x-1\\eq0\ \wedge\ x-7\\eq0\\\\\boxed{x\\eq0\ \wedge\ x\\eq1\ \wedge\ x\\eq7}\to\boxed{x\in\mathbb{R}-\{0,\ 1,\ 7\}}`