Domanda del libro di testo
Solve each linear equation. See Examples 1–3. 7x - 5x + 15 = x + 8
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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 13
Find the domain of each rational expression. See Example 1. (3x + 7) / (4x + 2) (x - 1)
Guida verificata passo dopo passo1
Identify the rational expression given: \(\frac{3x + 7}{(4x + 2)(x - 1)}\).
Recall that the domain of a rational expression excludes values of \(x\) that make the denominator equal to zero, because division by zero is undefined.
Set each factor in the denominator equal to zero to find the excluded values: solve \(4x + 2 = 0\) and \(x - 1 = 0\) separately.
Solve \(4x + 2 = 0\) by isolating \(x\): \(4x = -2\) then \(x = -\frac{1}{2}\); solve \(x - 1 = 0\) to get \(x = 1\).
Conclude that the domain is all real numbers except \(x = -\frac{1}{2}\) and \(x = 1\), since these values make the denominator zero.
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Domain of a Rational Expression
The domain of a rational expression includes all real numbers except those that make the denominator zero. Since division by zero is undefined, identifying values that cause the denominator to be zero is essential to determine the domain.
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Percorso guidato
2:58
Rationalizing Denominators
Factoring and Setting Denominator Equal to Zero
To find values excluded from the domain, factor the denominator if possible and set each factor equal to zero. Solving these equations reveals the values that make the denominator zero, which must be excluded from the domain.
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Percorso guidato
3:42Rationalizing Denominators Using Conjugates
Simplifying Rational Expressions
Simplifying the rational expression by canceling common factors can help in understanding the expression better, but it does not change the domain. The original restrictions from the denominator remain, regardless of simplification.
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Percorso guidato
2:58Rationalizing Denominators
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