Rational equations and inequalities

9000024106

Level:

Identify the optimal first step to solve the following equation. The operation is intended to be used on both sides of the equation. Assume \(x\neq 1\) and \(x\neq 2\). \[ \frac{1} {x - 1} = \frac{2} {x - 2} \]

multiply by \((x - 1)\cdot (x - 2)\)

multiply by \((x - 1)\)

multiply by \((x - 2)\)

multiply by \((x + 1)\)

multiply by \((x + 2)\)

multiply by \((x - 1)\cdot (x + 2)\)

9000024109

Level:

Identify the optimal first step to solve the following equation. The operation is intended to be used on both sides of the equation. \[ \frac{2x + 1} {x - 1} + \frac{x + 1} {x - 1} = \frac{11} {2} \]

multiply by \(2(x - 1)\), assuming \(x\neq 1\)

multiply by \((2x + 1)\), assuming \(x\neq -\frac{1} {2}\)

multiply by \((x + 1)\), assuming \(x\neq - 1\)

multiply by \(\frac{1} {2x+1}\), assuming \(x\neq -\frac{1} {2}\)

multiply by \(\frac{1} {x+1}\), assuming \(x\neq - 1\)

multiply by \(2(2x + 1)(x + 1)\), assuming \(x\neq -\frac{1} {2}\) and \(x\neq - 1\)

9000033301

Level:

Find the solution set of the following equation. \[ \frac{3x + 6} {2 - x} = 0 \]

\(\{ - 2\}\)

\(\emptyset \)

\(\{2\}\)

\(\mathbb{R}\setminus \{2\}\)

9000033302

Level:

Find the solution set of the following equation. \[ \frac{4x - 2} {2x - 1} = 2 \]

\(\mathbb{R}\setminus \left \{\frac{1} {2}\right \}\)

\(\mathbb{R}\)

\(\{2\}\)

\(\emptyset \)

9000033303

Level:

Find the solution set of the following equation. \[ \frac{4x + 8} {x + 2} = 0 \]

\(\emptyset \)

\(\{- 2\}\)

\(\{2\}\)

\(\left \{-\frac{3} {4}\right \}\)

9000079203

Level:

Find all real \(x\) for which the following expression equals zero. \[ 1 -\frac{2x + 1} {x - 1} \]

\(x = -2\)

\(x = -\frac{1} {2}\)

\(x = 0\)

\(x = -1\)

9000083701

Level:

Find all the values of \(x\in \mathbb{R}\) for which the given expression equals zero. \[ \frac{x^{2} - 16} {2x - 8} \]

\(x = -4\)

\(x = 4\)

\(x =\pm 4\)

\(x = 0\)

9000083702

Level:

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:

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:

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.

\(x = 0\)

\(x = 2\)

\(x = -2,\ x = 0\)

Rational equations and inequalities

9000024106

9000024109

9000033301

9000033302

9000033303

9000079203

9000083701

9000083702

9000083703

9000083704

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