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.
\[
\frac{4x + 8}
{x + 2} = 0
\]
\(\emptyset \)
\(\{- 2\}\)
\(\{2\}\)
\(\left \{-\frac{3}
{4}\right \}\)
9000033301
Level:
A
Find the solution set of the following equation.
\[
\frac{3x + 6}
{2 - x} = 0
\]
\(\{ - 2\}\)
\(\emptyset \)
\(\{2\}\)
\(\mathbb{R}\setminus \{2\}\)
9000033302
Level:
A
Find the solution set of the following equation.
\[
\frac{4x - 2}
{2x - 1} = 2
\]
\(\mathbb{R}\setminus \left \{\frac{1}
{2}\right \}\)
\(\mathbb{R}\)
\(\{2\}\)
\(\emptyset \)
9000033304
Level:
B
Find the solution set of the following inequality.
\[
\frac{x + 4}
{x + 2}\leq 0
\]
\([ - 4,-2)\)
\((-\infty ,-4] \cup [ 2,\infty )\)
\((-\infty ,-4)\cup (-2,\infty )\)
\((-4,-2] \)