Rational Inequalities: Problems with Solutions

By Prof. Hernando Guzman Jaimes (University of Zulia - Maracaibo, Venezuela)
Problem 1
Solve the following inequality:
$\frac{5}{x+8}<0$
Problem 2
Solve the following inequality
$\frac{10}{2x+5}\geq 0$
Problem 3
Solve for x
$\frac{1}{x^{2}-1}<0$
Problem 4
Solve:
$\frac{x-3}{x+2}<0$
Problem 5
$\frac{x+5}{x}\geq 0$
Problem 6
Determine the intervals, in which the inequality is true:
$\frac{2x+6}{x-3}\leq 0$
Problem 7
$\frac{3x-1}{x+2}>0$
Problem 8
$\frac{x+1}{x-1}+2>0$
Problem 9
$\frac{x-2}{x+3}\leq 1$
Problem 10
$\frac{2x-3}{5x+2}\geq -2$

Problem 11
$\frac{3x-1}{2x-1}<-4$
Problem 12
$x\leq 3-\frac{6}{x+2}$
Problem 13
$\frac{x\left(x-1\right) }{x+5}\geq 0$
Problem 14
$\frac{\left( 1+x\right) \left( 1-x\right) }{x}<0$
Problem 15
$\frac{x^{2}-2x+3}{x+1}\leq 1$
Problem 16
$\frac{x}{x^{2}-1}\geq 0$
Problem 17
$\frac{\left(x^{2}-1\right) }{\left( x^{2}-4\right) }\geq 0$
Problem 18
$\frac{2}{x-2}+\frac{3}{x-3}\leq 0$
Problem 19
$\frac{x^{2}+2x-3}{x^{2}-1}<0$
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