9000083701
Level:
A
Find all the values of \(x\in \mathbb{R}\)
for which the given expression equals zero.
\[
\frac{x^{2} - 16}
{2x - 8}
\]
\(x = -4\)
\(x = 4\)
\(x =\pm 4\)
\(x = 0\)
Rational equations and inequalities
9000083702
Level:
A
Find all the values of \(x\in \mathbb{R}\)
for which the given expression equals zero.
\[
\frac{x^{2} + 6x + 9}
{x^{2} - 9}
\]
The expression never equals zero.
\(x =\pm 3\)
\(x = 3\)
\(x = -3\)
9000083703
Level:
A
Find all the values of \(x\in \mathbb{R}\)
for which the given expression equals zero.
\[
\frac{x^{3} - x}
{x - 1}
\]
\(x = -1,\ x = 0\)
\(x = 0\)
\(x = 1\)
\(x = -1,\ x = 0,\ x = 1\)
9000083704
Level:
A
Find all the values of \(x\in \mathbb{R}\)
for which the given expression equals zero.
\[
\frac{x^{2} - 4x + 4}
{x(x - 2)}
\]
The expression never equals zero.
\(x = 0\)
\(x = 2\)
\(x = -2,\ x = 0\)
9000079203
Level:
A
Find all real \(x\)
for which the following expression equals zero.
\[
1 -\frac{2x + 1}
{x - 1}
\]
\(x = -2\)
\(x = -\frac{1}
{2}\)
\(x = 0\)
\(x = -1\)
9000039005
Level:
B
Find all the values of \(x\)
for which the following expression is positive.
\[
\frac{2x - 3}
{7 - 3x}
\]
\(x\in \left (\frac{3}
{2}; \frac{7}
{3}\right )\)
\(x\in \left (\frac{3}
{2};+\infty \right )\)
\(x\in \left (\frac{7}
{3};+\infty \right )\)
\(x\in (0;+\infty )\)
9000033303
Level:
A
Find the solution set of the following equation.
\[
\frac{4x + 8}
{x + 2} = 0
\]
\(\emptyset \)
\(\{- 2\}\)
\(\{2\}\)
\(\left \{-\frac{3}
{4}\right \}\)
9000033306
Level:
B
Find the solution set of the following inequality.
\[
\frac{2}
{3} < \frac{2 + x}
{3 + x}
\]
\((-\infty ;-3)\cup (0;\infty )\)
\(\mathbb{R}\)
\((-3;\infty )\)
\((-3;0)\)
9000033304
Level:
B
Find the solution set of the following inequality.
\[
\frac{x + 4}
{x + 2}\leq 0
\]
\([ - 4;-2)\)
\((-\infty ;-4] \cup [ 2;\infty )\)
\((-\infty ;-4)\cup (-2;\infty )\)
\((-4;-2] \)
9000033305
Level:
B
Find the solution set of the following inequality.
\[
\frac{2}
{x + 1}\geq 1
\]
\((-1;1] \)
\([ - 1;1)\)
\((-\infty ;-1)\cup [ 1;\infty )\)
\((-\infty ;1] \)