Rational equations and inequalities

2000005306

Level:

Use the graphs of the functions \(f(x)=x^2-4\) and \(g(x)=x+2\) to find the solution set of the following inequality. \[\frac{x^2-4}{x+2} \geq 0\]

\( x \in [ 2;+\infty) \)

\( x \in ( 2;+\infty) \)

\( x \in (-\infty;-2) \cup ( 2;+\infty) \)

\( x \in (-\infty;-2] \cup [ 2;+\infty) \)

2000005305

Level:

Find all real values of \(x\) such that the fraction \( \frac{7}{x^2+1} \) is negative.

\( \emptyset \)

\( x \in \mathbb{R} \)

\( x \in (-1;+\infty) \)

\( x \in \mathbb{R}\setminus \{ \pm 1\}\)

2000005304

Level:

Find all real values of \( x\) such that the fraction \( \frac{5}{x^2}\) is positive.

\( x \in \mathbb{R}\setminus \{0\}\)

\( x \in \mathbb{R}\)

\( x \in (0;+\infty)\)

\( x \in [ 0;+\infty)\)

2000005303

Level:

Use the graphs of the functions \( f(x)=x^2-5x+4\) and \(g(x)=x^2+2x-3\) to find the solution set of the following equation. \[ \frac{x^2-5x+4}{x^2+2x-3}=1\]

\( \emptyset\)

\( \{1\}\)

\( \{-3;4\}\)

\( \{-3;1;4\}\)

2000005302

Level:

Use the graphs of the functions \(f(x)=x^2-x-6\) and \(g(x)=x-3\) to find the solution set of the following equation. \[\frac{x^2-x-6}{x-3}=1\]

\( \{ -1\} \)

\( \{ 3\} \)

\( \{ -1;3\} \)

\( \{ -2;3\} \)

2000005301

Level:

In real numbers, find the solution set of the following equation. \[\frac{x^2+1}{x^2-9}=0\]

\( \emptyset \)

\( \pm 1\)

\( \pm 3\)

\( -1\)

Rational Inequalities I

Submitted by ladislav.foltyn on Sat, 03/02/2019 - 16:48