9000083707
Level:
A
Find all the values of \(x\in \mathbb{R}\)
for which the given expression equals zero.
\[
\frac{4x^{3} + 20x^{2} + 25x}
{x + 1}
\]
\(x = 0,\ x = -\frac{5}
{2}\)
\(x = 0\)
\(x = -\frac{5}
{2}\)
\(x = -1\)
Rational Equations and Inequalities
9000083708
Level:
A
Find all the values of \(x\in \mathbb{R}\)
for which the given expression equals zero.
\[
\frac{x^{2} - (2x - 1)^{2}}
{x^{2} - 4}
\]
\(x = \frac{1}
{3},\ x = 1\)
\(x = -\frac{1}
{3},\ x = 1\)
\(x =\pm 2\)
\(x = 1\)
9000083709
Level:
A
Find all the values of \(x\in \mathbb{R}\)
for which the given expression equals zero.
\[
\frac{(2x + 3)^{2} - (3x - 2)^{2}}
{x - 5}
\]
\(x = -\frac{1}
{5}\)
\(x = 5\)
\(x = -5\)
\(x = \frac{1}
{5}\)
9000083710
Level:
A
Find all the values of \(x\in \mathbb{R}\)
for which the given expression equals zero.
\[
\frac{(4x + 3)^{2} - (5x - 2)^{2}}
{5 + x}
\]
\(x = 5,\ x = -\frac{1}
{9}\)
\(x = -5\)
\(x = -\frac{5}
{9},\ x = 1\)
\(x = 1,\ x = \frac{5}
{9}\)
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.
\[
\frac{2x - 3}
{7 - 3x}
\]
\(x\in \left (\frac{3}
{2}, \frac{7}
{3}\right )\)
\(x\in \left (\frac{3}
{2},+\infty \right )\)
\(x\in \left (\frac{7}
{3},+\infty \right )\)
\(x\in (0,+\infty )\)
9000033306
Level:
B
Find the solution set of the following inequality.
\[
\frac{2}
{3} < \frac{2 + x}
{3 + x}
\]
\((-\infty ,-3)\cup (0,\infty )\)
\(\mathbb{R}\)
\((-3,\infty )\)
\((-3,0)\)
9000033307
Level:
B
Find the solution set of the following inequality.
\[
\frac{4}
{x^{2} - x - 6}\leq 0
\]
\((-2,3)\)
\(\mathbb{R}\)
\((-\infty ,-2)\cup (3,\infty )\)
\((-3,2)\)
9000033308
Level:
C
Find the solution set of the following inequality.
\[
\frac{x^{2} + x + 2}
{x^{2} + 4x + 3}\geq 0
\]
\((-\infty ,-3)\cup (-1,\infty )\)
\((1,3)\)
\((-\infty ,1)\cup (3,\infty )\)
\((-3,-1)\)
9000033303
Level:
A
Find the solution set of the following equation.
\[
\frac{4x + 8}
{x + 2} = 0
\]
\(\emptyset \)
\(\{- 2\}\)
\(\{2\}\)
\(\left \{-\frac{3}
{4}\right \}\)