2000005301
Level:
A
In real numbers, find the solution set of the following equation.
\[\frac{x^2+1}{x^2-9}=0\]
\( \emptyset \)
\( \pm 1\)
\( \pm 3\)
\( -1\)
Rational Equations and Inequalities
1003019801
Level:
A
Find the domain of the expression.
\[
\frac{x^2+4x-5}{-3x^2-19x+14}
\]
\(\mathbb{R}\setminus\left\{-7,\frac23\right\}\)
\(\mathbb{R}\setminus\left\{7,-\frac23\right\}\)
\(\left(7,-\frac23\right)\)
\(\left(-7,\frac23\right)\)
1003044806
Level:
A
Find the domain of the equation \( \frac{(x-1)(x+2)}{(x-1)(x+3)}=\frac1x \).
\( \mathbb{R}\setminus\{-3,0,1\} \)
\( \mathbb{R}\setminus\{-3,0\} \)
\( \mathbb{R}\setminus\{-3,-2,0\} \)
\( \mathbb{R}\setminus\{-3,1\} \)
1003044807
Level:
A
Find the domain of the equation \( \frac{x+1}{x^2-3}=\frac{x^2+x-2}{2x+8} \).
\( \mathbb{R}\setminus\{-4,-\sqrt3,\sqrt3\} \)
\( \mathbb{R}\setminus\{-2,-1,1\} \)
\( \mathbb{R}\setminus\{-4,\sqrt3\} \)
\( \mathbb{R}\setminus\{-4\} \)
1003044808
Level:
A
Find the domain of the equation \( \frac{3x+2}{\frac x3}=1 \).
\( \mathbb{R}\setminus \{0\} \)
\( \mathbb{R} \)
\( \mathbb{R}\setminus \{-\frac23\} \)
\( \mathbb{R}\setminus \{-\frac23,0\} \)
1003044809
Level:
A
Find the domain of the equation \( \frac{2x+5}{x-2}=\frac1{x^2-1} \).
\( \mathbb{R}\setminus\{-1,1,2\} \)
\( \mathbb{R}\setminus\{1,2\} \)
\( \mathbb{R}\setminus\{-\frac52,-1,1\} \)
\( \mathbb{R}\setminus\{2\} \)
1003044810
Level:
A
Find the domain of the equation \( \frac{x+3}{x^2-8}=\frac1x \).
\( \mathbb{R}\setminus\{-2\sqrt2,0,2\sqrt2\} \)
\( \mathbb{R}\setminus\{0\} \)
\( \mathbb{R}\setminus\{-3\} \)
\( \mathbb{R}\setminus\{0,4\} \)
1003119001
Level:
A
Find the solution set of the following equation.
\[ \frac{x+1}{x-1}=0 \]
\( \{-1\} \)
\( \{-1,1\} \)
\( \{-1,0,1\} \)
\( \emptyset \)
1003119002
Level:
A
Find the solution set of the following equation.
\[ \frac{x^2+4x+4}{x+2}=0 \]
\( \emptyset \)
\( \{-2\} \)
\( \{-2,2\} \)
\( \{2\} \)
1003119003
Level:
A
Find the solution set of the following equation.
\[ \frac{3x^2-27}{x+3}=0 \]
\( \{ 3 \} \)
\( \{ -3,3 \} \)
\( \{ 9 \} \)
\( \emptyset \)