Rational equations and inequalities

9000022804

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

9000021804

Level: 
B
Solve the following inequality. \[ \frac{1} {x - 3}\leq \frac{1} {2 - x} \]
\(x\in (-\infty ;2)\cup \left [ \frac{5} {2};3\right )\)
\(x\in (-\infty ;2)\cup \left [ \frac{5} {3};2\right ] \)
\(x\in \left (-\infty ; \frac{5} {2}\right ] \cup \left (3;\infty \right )\)
\(x\in \left [ \frac{5} {2};\infty \right )\)

9000021810

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