Domanda del libro di testo
Evaluate each expression. See Example 5. -|-2|
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Ch. R - Algebra Review
Lial12th EditionTrigonometryISBN: 9780136552161, 9780135440780, 9780136881117, 9780135440827, 9780135924891
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TOC.tableOfContents
- 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
Lial12th EditionTrigonometryISBN: 9780136552161, 9780135440780, 9780136881117, 9780135440827, 9780135924891Non è quello che usi tu?Cambia libro di testo
Capitolo 1, Problema 61
Add or subtract, as indicated. See Example 4. (3/a - 2) - (1/2 - a)
Guida verificata passo dopo passo1
Identify the given expression: \(\frac{3}{a - 2} - \frac{1}{2 - a}\).
Notice that the denominators \(a - 2\) and \(2 - a\) are related. Recall that \(2 - a = -(a - 2)\), so rewrite the second fraction as \(\frac{1}{2 - a} = \frac{1}{-(a - 2)} = -\frac{1}{a - 2}\).
Substitute this back into the expression to get \(\frac{3}{a - 2} - \left(-\frac{1}{a - 2}\right)\), which simplifies to \(\frac{3}{a - 2} + \frac{1}{a - 2}\).
Since both fractions now have the same denominator, combine the numerators: \(\frac{3 + 1}{a - 2} = \frac{4}{a - 2}\).
The simplified expression is \(\frac{4}{a - 2}\). This is the combined result of the original subtraction.
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Finding a Common Denominator
When adding or subtracting fractions, it is essential to express them with a common denominator. This allows the numerators to be combined directly. For algebraic fractions, the common denominator is typically the least common multiple of the individual denominators.
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Percorso guidato
2:58
Rationalizing Denominators
Simplifying Algebraic Expressions
After combining fractions, simplifying the resulting algebraic expression involves factoring and reducing terms. This step ensures the expression is in its simplest form, making it easier to interpret or use in further calculations.
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Percorso guidato
6:36Simplifying Trig Expressions
Handling Variable Expressions in Denominators
When denominators contain variables, special care is needed to avoid division by zero and to correctly manipulate expressions. Understanding how to factor and find common denominators involving variables is crucial for accurate addition or subtraction.
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Percorso guidato
2:58Rationalizing Denominators
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