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Simplify each rational expression. Find all numbers that must be excluded from the domain of the simplified rational expression.
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Ch. P - Fundamental Concepts of Algebra
Blitzer8th EditionCollege AlgebraISBN: 9780136970514
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TOC.tableOfContents
- Ch. P - Fundamental Concepts of Algebra311
- Ch. 1 - Equations and Inequalities398
- Ch. 2 - Functions and Graphs407
- Ch. 3 - Polynomial and Rational Functions306
- Ch. 4 - Exponential and Logarithmic Functions247
- Ch. 5 - Systems of Equations and Inequalities173
- Ch. 6 - Matrices and Determinants143
- Ch. 7 - Conic Sections124
- Ch. 8 - Sequences, Induction, and Probability251
Capitolo 1, Problema 10
Rewrite each expression without the absolute value bars. |√2-1|
Guida verificata passo dopo passo1
Recall that the absolute value of a number \(x\), denoted \(|x|\), is defined as \(x\) if \(x \geq 0\), and \(-x\) if \(x < 0\).
Identify the expression inside the absolute value bars: \(\sqrt{2} - 1\).
Determine whether \(\sqrt{2} - 1\) is nonnegative or negative by approximating \(\sqrt{2}\). Since \(\sqrt{2} \approx 1.414\), then \(\sqrt{2} - 1 \approx 0.414\), which is positive.
Since \(\sqrt{2} - 1 \geq 0\), the absolute value expression \(|\sqrt{2} - 1|\) can be rewritten without the absolute value bars as \(\sqrt{2} - 1\).
Therefore, the expression without absolute value bars is simply \(\sqrt{2} - 1\).
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Absolute Value Definition
The absolute value of a number represents its distance from zero on the number line, always yielding a non-negative result. For any real number x, |x| equals x if x is non-negative, and -x if x is negative.
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Vertex Form
Evaluating Square Roots
The square root function, √x, returns the non-negative number whose square is x. Since √2 is approximately 1.414, it is positive, which helps determine the sign of expressions involving square roots.
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02:20Imaginary Roots with the Square Root Property
Simplifying Expressions Inside Absolute Value
To rewrite an expression without absolute value bars, first evaluate or estimate the expression inside. If the expression is positive or zero, the absolute value can be removed directly; if negative, multiply by -1 to remove the bars.
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05:07Simplifying Algebraic Expressions
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