Textbook Question
Add or subtract, as indicated. See Example 6. √6 + √6
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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 87
Simplify each complex fraction. See Examples 5 and 6. (1/(x + 1) − 1/x) / (1/x)
Verified step by step guidance1
Rewrite the complex fraction clearly to understand its structure. The expression is: \(\frac{\frac{1}{x+1} - \frac{1}{x}}{\frac{1}{x}}\).
Focus on simplifying the numerator first: \(\frac{1}{x+1} - \frac{1}{x}\). Find a common denominator for these two fractions, which is \(x(x+1)\).
Rewrite each fraction in the numerator with the common denominator: \(\frac{x}{x(x+1)} - \frac{x+1}{x(x+1)}\).
Combine the fractions in the numerator by subtracting the numerators over the common denominator: \(\frac{x - (x+1)}{x(x+1)}\).
Simplify the numerator of the combined fraction and then divide this result by the denominator \(\frac{1}{x}\) by multiplying by its reciprocal.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Complex Fractions
A complex fraction is a fraction where the numerator, denominator, or both contain fractions themselves. Simplifying involves rewriting the expression as a single fraction by finding common denominators or multiplying numerator and denominator by the least common denominator to eliminate smaller fractions.
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Dividing Complex Numbers
Algebraic Manipulation
Algebraic manipulation includes operations like factoring, expanding, and simplifying expressions. In this context, it is essential to carefully handle variables and expressions in both numerator and denominator to combine terms correctly and reduce the fraction to its simplest form.
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04:12Algebraic Operations on Vectors
Fraction Division and Multiplication
Dividing fractions involves multiplying by the reciprocal of the divisor. When simplifying complex fractions, converting division into multiplication by the reciprocal helps to combine and simplify the expression efficiently.
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4:02Solving Linear Equations with Fractions
Related Practice
Textbook Question
Add or subtract, as indicated. See Example 6. 5√3 - √3
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Textbook Question
Factor each polynomial completely. See Example 6. 8t³ + 125
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Textbook Question
Use an inequality symbol to write each statement. 5 + 0 is not equal to 0.
Textbook Question
Factor each polynomial completely. See Example 6. 4m²p - 12mnp + 9n²p
Textbook Question
Simplify each inequality if needed. Then determine whether the statement is true or false. 0 ≤ -5
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