5.2 Rational inequalities

How many negative integer solutions does the inequality [math]\displaystyle{\frac{(x^3+1)(x+3)x}{x^4-1}}\geq0[/math] have?

What is the greatest integer solution to the inequality [math]\displaystyle{\frac{x^4+x^3+x^2}{x^3-5x^2-6x}}\leq0[/math]?

Which of the following is the solution to the inequality [math]\displaystyle{x^2+\frac{1}{x^2}>\frac{2}{x^4}}[/math]?

If [math]\displaystyle{\frac{1}{\frac{1}{x+1}+\frac{1}{x-1}}}[/math] is always greater than 5 when [math]x>5+\sqrt{a}[/math] where [math]a[/math] is a positive integer, what is the value of [math]a[/math]?

Which of the following intervals is not a part of the solution to the inequality [math]\dfrac{(x-1)(x-2)^2x^2}{(x-1)(x-2)(x+3)}\geq0[/math]?

Which of the following intervals is the solution to the inequality [math]\dfrac{x^2+4x+5}{x+2}\leq1[/math]?

The solution to the inequality [math]\dfrac{x^4-18x^2+81}{x^2+9}>0[/math] is all real numbers except for [math]x=n[/math] where [math]n[/math] is an integer. What is the maximum of [math]n[/math]?

How many positive integer solution does the inequality [math]\dfrac{x-1}{x-2}\leq\dfrac{x-2}{x-1}[/math] have?

Consider a rational function [math]f(x)=\dfrac{(x+3)(x-2)^2(x+1)^2}{x^3-8}[/math]. Which of the following values is positive?

How many integer solutions does the inequality [math]\dfrac{(x+2)(x-1)(x+3)}{(x+2)(x^2+4x+5)}\leq0[/math] have?

If [math]x=\dfrac{a}{7}[/math] is \textbf{not} a solution to the inequality [math]\dfrac{(x-1)^2(x-3)}{(x-2)}>0[/math] where [math]a[/math] is an integer, what is the minimum of [math]a[/math]?

How many negative integer solutions does the inequality [math]\dfrac{1}{x^2-1}>\dfrac{4}{x^2-6x+5}[/math] have?

The solution to the inequality [math]\dfrac{1}{x+1}>1-x[/math] is [math]x>-1[/math] except for [math]x[/math] is

If [math]1-\dfrac{2}{x-1}\leq\dfrac{1}{x}[/math], what is the maximum of [math]x[/math]?

If [math]x<a[/math] is the solution to [math]\dfrac{x^2-3}{x-2}<6[/math], what is [math]a[/math]?