which shows all the critical points for the inequality $\frac{x^{2}-9x}{x - 5}<0$?\n$x = 5$\n$x = 0$ and $x…

which shows all the critical points for the inequality $\frac{x^{2}-9x}{x - 5}<0$?\n$x = 5$\n$x = 0$ and $x = 9$\n$x = 0,x = 5$, and $x = 9$\n$x=-3,x = 0,x = 3$, and $x = 5$
Answer
Explanation:
Step1: Find the zero - points of the numerator
Set the numerator $x^{2}-9x = 0$. Factor out $x$: $x(x - 9)=0$. Then $x=0$ or $x = 9$ by the zero - product property.
Step2: Find the zero - point of the denominator
Set the denominator $x - 5=0$. Solving for $x$ gives $x = 5$. The function is undefined at $x = 5$.
Answer:
$x = 0,x = 5$, and $x = 9$