About Rational Expressions:
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. We simplify a rational expression by first factoring the numerator and denominator and then canceling common factors.
Test Objectives
- Demonstrate the ability to solve a quadratic equation by factoring
- Demonstrate the ability to find the restricted values for a rational expression
- Demonstrate the ability to simplify a rational expression
#1:
Instructions: Find the domain.
a)$$f(x)=\frac{x^2 + 3x - 4}{-3x - 3}$$
b)$$h(x)=\frac{x^2 + 2x - 8}{4x - 7}$$
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#2:
Instructions: Find the domain.
a)$$f(x)=\frac{x^2 - x}{-2x^3 + 4x^2 + 6x}$$
b)$$h(x)=\frac{6x^4 - 66x^3 + 60x^2}{4x^3 - 36x}$$
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#3:
Instructions: Simplify each.
a)$$\frac{r - 1}{r^2 - 4r + 3}$$
b)$$\frac{3m - 9}{3 - m}$$
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#4:
Instructions: Simplify each.
a)$$\frac{5k + 35}{10k^2 + 60k - 70}$$
b)$$\frac{n^3 + 4n^2 - 32n}{n^2 + 12n + 32}$$
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#5:
Instructions: Simplify each.
a)$$\frac{5n^2 + 15n + 10}{-n^2 - 3n - 2}$$
b)$$\frac{5x^2 + 6x + 1}{6x^2 + 8x + 2}$$
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Written Solutions:
#1:
Solutions:
a)$$\left\{x|x≠ -1\right\}$$
b)$$\left\{x|x≠ \frac{7}{4}\right\}$$
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#2:
Solutions:
a)$$\left\{x|x≠ -1,0,3\right\}$$
b)$$\left\{x|x≠ -3,0,3\right\}$$
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#3:
Solutions:
a)$$\frac{1}{r - 3}$$
b)$$-3$$
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#4:
Solutions:
a)$$\frac{1}{2(k - 1)}$$
b)$$\frac{n(n - 4)}{n + 4}$$
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#5:
Solutions:
a)$$-5$$
b)$$\frac{5x + 1}{2(3x + 1)}$$
