Textbook Question
Solve each quadratic equation using the zero-factor property. See Example 5. -4x² + x = -3
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Ch. R - Algebra Review
Lial12th EditionTrigonometryISBN: 9780136552161
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Table of contents
- Ch. R - Algebra Review381
- Ch. 1 - Trigonometric Functions188
- Ch. 2 - Acute Angles and Right Triangles168
- Ch. 3 - Radian Measure and The Unit Circle155
- Ch. 4 - Graphs of the Circular Functions100
- Ch. 5 - Trigonometric Identities238
- Ch. 6 - Inverse Circular Functions and Trigonometric Equations158
- Ch. 7 - Applications of Trigonometry and Vectors148
- Ch. 8 - Complex Numbers, Polar Equations, and Parametric Equations15
Chapter 1, Problem 7
CONCEPT PREVIEW Perform the indicated operation, and write each answer in lowest terms 3 7 —— + —— x x
Verified step by step guidance1
Identify the given expression as the sum of two fractions with the same denominator: \(\frac{3}{x} + \frac{7}{x}\).
Since the denominators are the same, combine the numerators directly over the common denominator: \(\frac{3 + 7}{x}\).
Add the numerators: \(3 + 7 = 10\), so the expression becomes \(\frac{10}{x}\).
Check if the fraction \(\frac{10}{x}\) can be simplified further by factoring numerator and denominator and canceling common factors.
Write the final simplified expression, ensuring it is in lowest terms.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Adding Rational Expressions
Adding rational expressions involves combining fractions with variables in the denominators. To add them, you must find a common denominator, rewrite each fraction with this denominator, and then add the numerators while keeping the denominator the same.
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2:58
Rationalizing Denominators
Finding the Least Common Denominator (LCD)
The least common denominator is the smallest expression that both denominators divide into evenly. For variable denominators like 'x', the LCD is simply 'x' if both denominators are the same, which allows direct addition of the numerators.
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3:42Rationalizing Denominators Using Conjugates
Simplifying Rational Expressions
After performing the addition, simplify the resulting rational expression by factoring and reducing common factors in the numerator and denominator. This ensures the answer is in lowest terms, making it easier to interpret and use.
Recommended video:
2:58Rationalizing Denominators
Related Practice
Textbook Question
Solve each quadratic equation using the quadratic formula. See Example 7. -2x² + 4x + 3 = 0
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Textbook Question
CONCEPT PREVIEW Perform the operations mentally, and write the answers without doing intermediate steps. √25 + √64
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Textbook Question
Determine whether each equation is an identity, a conditional equation, or a contradiction. Give the solution set. See Example 4. -2(x + 3) = -6(x + 7)
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Textbook Question
CONCEPT PREVIEW Fill in the blank(s) to correctly complete each sentence. The midpoint of the segment joining (0, 0) and (4, 4) is ________.
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Textbook Question
CONCEPT PREVIEW Evaluate each expression. 10³