A rational expression is the quotient of two polynomials, where the denominator is not equal to zero. When we first work with rational expressions, we encounter two tasks: find the restricted values and simplify. We find the restricted values by identifying what values create a denominator of zero.

Test Objectives
• Demonstrate the ability to find the domain of a rational expression
Rational Expressions Restricted Values Practice Test:

#1:

Instructions: Find the domain.

$$a)\hspace{.2em}\frac{8x - 4}{16}$$

$$b)\hspace{.2em}\frac{20x^2 - 8x}{8x^3}$$

#2:

Instructions: Find the domain.

$$a)\hspace{.2em}\frac{x^2 + 9x + 8}{x^2 + 18x + 80}$$

$$b)\hspace{.2em}\frac{x^2 + x - 42}{3x + 21}$$

#3:

Instructions: Find the domain.

$$a)\hspace{.2em}\frac{8x + 64}{x^2 - x - 72}$$

$$b)\hspace{.2em}\frac{3x^2 - 27x - 30}{4x^3 - 20x^2 - 200x}$$

#4:

Instructions: Find the domain.

$$a)\hspace{.2em}\frac{14x^2 - 90x - 56}{2x^2 - 7x - 49}$$

$$b)\hspace{.2em}\frac{15x^3 + 3x^2 - 12x}{2x^3 - 4x^2 - 6x}$$

#5:

Instructions: Find the domain.

$$a)\hspace{.2em}\frac{9x + 27}{9x^2 + 6x - 3}$$

$$b)\hspace{.2em}\frac{6x^2 - 2x - 4}{7x^2 - 11x + 4}$$

Written Solutions:

#1:

Solutions:

$$a)\hspace{.2em}\{x | x ∈ \mathbb{R}\}$$

$$b)\hspace{.2em}\{x | x ≠ 0\}$$

#2:

Solutions:

$$a)\hspace{.2em}\{x | x ≠ -10, -8\}$$

$$b)\hspace{.2em}\{x | x ≠ -7\}$$

#3:

Solutions:

$$a)\hspace{.2em}\{x | x ≠ -8, 9\}$$

$$b)\hspace{.2em}\{x | x ≠ -5, 0, 10\}$$

#4:

Solutions:

$$a)\hspace{.2em}\left\{x | x ≠ -\frac{7}{2}, 7 \right\}$$

$$b)\hspace{.2em}\{x | x ≠ -1, 0, 3\}$$

#5:

Solutions:

$$a)\hspace{.2em}\left\{x | x ≠ -1, \frac{1}{3} \right\}$$

$$b)\hspace{.2em}\left\{x | x ≠ \frac{4}{7}, 1 \right\}$$