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9000083605

Level:

Find the common denominator of the fractions. \[ \text{$ \frac{3x} {x^{2}+4x+4}$ and $ \frac{x+5} {x^{2}-4}$} \]

$(x + 2)^{2}(x - 2),\; x\neq \pm 2$

$(x + 2)(x - 4),\; x\neq \pm 2$

$(x + 2)^{2}(x - 4),\; x\neq \pm 2$

$(x + 2)(x - 4),\; x\neq \pm 2$

9000081402

Level:

Find the inequality which describes the set graphed in the picture.

$|x - 1| < 2;\ x\in \mathbb{R}$

$|x + 1| < 2;\ x\in \mathbb{R}$

$|x - 1| > 2;\ x\in \mathbb{R}$

$|x + 1| > 2;\ x\in \mathbb{R}$

$|x - 2| > 1;\ x\in \mathbb{R}$

9000083603

Level:

Evaluate the following expression at $x = \frac{1} {2}$ and $y = -\frac{1} {4}$. \[ \frac{x -\frac{y} {x}} {1 + \frac{x} {y}} \]

$- 1$

$3$

$4$

$1$

9000081403

Level:

Find the inequality which describes the set graphed in the picture.

$|x + 1| > 2;\ x\in \mathbb{R}$

$|x - 1| < 2;\ x\in \mathbb{R}$

$|x + 1| < 2;\ x\in \mathbb{R}$

$|x - 1| > 2;\ x\in \mathbb{R}$

$|x - 2| > 1;\ x\in \mathbb{R}$

9000083604

Level:

Assuming $x\neq - 1$, $x\neq \pm y$, simplify the expression. \[ \frac{x^{2} + 2xy + y^{2}} {2x^{2} + 4x + 2} \cdot \frac{(x + 1)(y - x)} {y^{2} - x^{2}} \]

$\frac{x+y} {2x+2}$

$\frac{x+y} {2} $

$x + y$

$\frac{1} {2}$

9000081404

Level:

Find the inequality which describes the set graphed in the picture.

$|2 + x| > 1;\ x\in \mathbb{R}$

$|2 + x| < 1;\ x\in \mathbb{R}$

$|2 - x| > 1;\ x\in \mathbb{R}$

$|2 - x| < 1;\ x\in \mathbb{R}$

$|1 + x| > 2;\ x\in \mathbb{R}$

9000081405

Level:

Find the inequality which describes the set graphed in the picture.

$|2 - x| < 1;\ x\in \mathbb{R}$

$|2 + x| > 1;\ x\in \mathbb{R}$

$|2 + x| < 1;\ x\in \mathbb{R}$

$|2 - x| > 1;\ x\in \mathbb{R}$

$|1 - x| < 2;\ x\in \mathbb{R}$

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. \[ \frac{x^{3} - x} {x - 1} \]

$x = -1,\ x = 0$

$x = 0$

$x = 1$

$x = -1,\ x = 0,\ x = 1$

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