9000083705
Level:
A
Find all the values of \(x\in \mathbb{R}\)
for which the given expression equals zero.
\[
\frac{2x(x + 2)(x - 3)}
{x^{2} - 4}
\]
\(x = 0,\ x = 3\)
\(x = -2,\ x = 0,\ x = 3\)
\(x = 0\)
\(x =\pm 2\)
Rational equations and inequalities
9000083706
Level:
A
Find all the values of \(x\in \mathbb{R}\)
for which the given expression equals zero.
\[
\frac{4x^{2} - 36}
{4x^{2} + 24x + 36}
\]
\(x = 3\)
\(x = 4\)
\(x = -3,\ x = 3\)
The expression never equals zero.
9000083707
Level:
A
Find all the values of \(x\in \mathbb{R}\)
for which the given expression equals zero.
\[
\frac{4x^{3} + 20x^{2} + 25x}
{x + 1}
\]
\(x = 0,\ x = -\frac{5}
{2}\)
\(x = 0\)
\(x = -\frac{5}
{2}\)
\(x = -1\)
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.
\[
\frac{(4x + 3)^{2} - (5x - 2)^{2}}
{5 + x}
\]
\(x = 5,\ x = -\frac{1}
{9}\)
\(x = -5\)
\(x = -\frac{5}
{9},\ x = 1\)
\(x = 1,\ x = \frac{5}
{9}\)
1003029001
Level:
B
Find the solution set of the inequality.
\[ \left(x^2+1\right)\left(x^2+3\right)\geq0 \]
\( \mathbb{R} \)
\( (-\infty;-1]\cup[1;\infty) \)
\( (-\infty;-1)\cup(1;\infty) \)
\( (-\infty;-\sqrt3]\cup[\sqrt3;\infty) \)
\( \emptyset \)
1003029101
Level:
B
Find the solution set of the inequality.
\[ \frac{x^4-1}{x\left(x^2+3\right)}\geq0 \]
\( [-1;0)\cup[1;\infty) \)
\( [-1;0]\cup[1;\infty) \)
\( (-\infty;0)\cup[1;\infty) \)
\( (-\infty;0]\cup[1;\infty) \)
1003029102
Level:
B
Find the solution set of the inequality.
\[ \frac{x\left(x^3-8\right)}{-x^4-4}\leq0 \]
\( (-\infty;0]\cup[2;\infty) \)
\( [ 0;2 ] \)
\( (-\infty;-2]\cup[0;2] \)
\( (-\infty;-2]\cup[2;\infty) \)
1003029103
Level:
B
Find the domain of the expression on the left side of the inequality.
\[\frac{x^4}{x^2\left(x^5-1\right)\left(2x^2-4\right)}\leq0 \]
\( \mathbb{R}\setminus\left\{0;1;\pm\sqrt2\right\}\)
\( \mathbb{R}\setminus\left\{1;\pm\sqrt2\right\}\)
\( \mathbb{R}\setminus\left\{\pm1;\pm\sqrt2\right\}\)
\( \mathbb{R}\setminus\left\{0;\pm1;\pm\sqrt2\right\}\)