About Rational Expressions Restricted Values:
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
#1:
Instructions: Find the domain.
$$a)\hspace{.2em}\frac{8x - 4}{16}$$
$$b)\hspace{.2em}\frac{20x^2 - 8x}{8x^3}$$
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#2:
Instructions: Find the domain.
$$a)\hspace{.2em}\frac{x^2 + 9x + 8}{x^2 + 18x + 80}$$
$$b)\hspace{.2em}\frac{x^2 + x - 42}{3x + 21}$$
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#3:
Instructions: Find the domain.
$$a)\hspace{.2em}\frac{8x + 64}{x^2 - x - 72}$$
$$b)\hspace{.2em}\frac{3x^2 - 27x - 30}{4x^3 - 20x^2 - 200x}$$
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#4:
Instructions: Find the domain.
$$a)\hspace{.2em}\frac{14x^2 - 90x - 56}{2x^2 - 7x - 49}$$
$$b)\hspace{.2em}\frac{15x^3 + 3x^2 - 12x}{2x^3 - 4x^2 - 6x}$$
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#5:
Instructions: Find the domain.
$$a)\hspace{.2em}\frac{9x + 27}{9x^2 + 6x - 3}$$
$$b)\hspace{.2em}\frac{6x^2 - 2x - 4}{7x^2 - 11x + 4}$$
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Written Solutions:
#1:
Solutions:
$$a)\hspace{.2em}\{x | x ∈ \mathbb{R}\}$$
$$b)\hspace{.2em}\{x | x ≠ 0\}$$
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#2:
Solutions:
$$a)\hspace{.2em}\{x | x ≠ -10, -8\}$$
$$b)\hspace{.2em}\{x | x ≠ -7\}$$
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#3:
Solutions:
$$a)\hspace{.2em}\{x | x ≠ -8, 9\}$$
$$b)\hspace{.2em}\{x | x ≠ -5, 0, 10\}$$
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#4:
Solutions:
$$a)\hspace{.2em}\left\{x | x ≠ -\frac{7}{2}, 7 \right\}$$
$$b)\hspace{.2em}\{x | x ≠ -1, 0, 3\}$$
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#5:
Solutions:
$$a)\hspace{.2em}\left\{x | x ≠ -1, \frac{1}{3} \right\}$$
$$b)\hspace{.2em}\left\{x | x ≠ \frac{4}{7}, 1 \right\}$$
