Rational Equations and Inequalities

9000021810

Level: 
B
Find all the values of \(x\) for which the following expression takes on values smaller than or equal to \(1\). \[ \frac{x + 1} {x - 1} - \frac{1} {x + 1} \]
\(x\in (-\infty ,-3] \cup (-1,1)\)
\(x\in (-\infty ,-3] \)
\(x\in (-\infty ,-1)\cup (-1,1)\cup (1,\infty )\)
\(x\in [ - 3,-1)\)

9000022804

Level: 
B
Establish the values of the real parameter \(t\) which ensure that the following expression is nonpositive. \[ \frac{2} {2t^{2} + t - 1} \]
\(\left (-1, \frac{1} {2}\right )\)
\(\left [ -\frac{1} {2},1\right ] \)
\(\left [ -1, \frac{1} {2}\right ] \)
\(\left (-\frac{1} {2},1\right )\)

9000039005

Level: 
B
Find all the values of \(x\) for which the following expression is positive. \[ \frac{2x - 3} {7 - 3x} \]
\(x\in \left (\frac{3} {2}, \frac{7} {3}\right )\)
\(x\in \left (\frac{3} {2},+\infty \right )\)
\(x\in \left (\frac{7} {3},+\infty \right )\)
\(x\in (0,+\infty )\)