Rational equations and inequalities

1103044804

Level: 
A
Given graphs of the functions \( f(x) = x^2-x-6 \) and \( g(x) = x+2 \), find the domain of the equation \( \frac{x+2}{x^2-x-6}=\frac{x^2-x-6}{x+2} \).
\( \mathbb{R}\setminus\{-2;3\} \)
\( \mathbb{R}\setminus\{-2;3;4\} \)
\( \mathbb{R}\setminus\{-2\} \)
\( \mathbb{R}\setminus\{-2;4\} \)

1103044805

Level: 
A
Given graphs of the functions \( f(x)=-x^2-x+6 \) and \( g(x) =x^2-4x+4 \), find the domain of the equation \( \frac{-x^2-x+6}{x^2-4x+4} =-2 \).
\( \mathbb{R}\setminus\{2\} \)
\( \mathbb{R}\setminus\{-3;2\} \)
\( \mathbb{R}\setminus\{-3;-0.5;2\} \)
\( \mathbb{R}\setminus\{-2\} \)

2010012104

Level: 
A
Given graphs of the functions \( f(x)= x^2+x-6 \) and \( g(x) = x-2 \), find the domain of the equation \( \frac{x-2}{x^2+x-6}=1 \).
\(\mathbb{R}\setminus \left \{-3;2\right \}\)
\(\mathbb{R}\setminus \left \{-2;2\right \}\)
\(\mathbb{R}\setminus \left \{-3;-2;2\right \}\)
\(\mathbb{R}\setminus \left \{0\right \}\)

9000024105

Level: 
A
Identify the optimal first step to solve the following equation. The operation is intended to be used on both sides of the equation. \[ \frac{4 + x} {x + 1} = \frac{x - 3} {x + 2} \]
multiply by \((x + 2)\cdot (x + 1)\), assuming \(x\neq - 2\) and \(x\neq - 1\)
multiply by \((4 + x)\cdot (x - 3)\), assuming \(x\neq - 4\) and \(x\neq 3\)
multiply by \((4 + x)\cdot (x + 1)\), assuming \(x\neq - 4\) and \(x\neq - 1\)
multiply by \((x - 3)\cdot (x + 2)\), assuming \(x\neq 3\) and \(x\neq - 2\)
multiply by \((x - 3)\), assuming \(x\neq 3\)
multiply by \((4 + x)\), assuming \(x\neq - 4\)