Domanda del libro di testo
Simplify each exponential expression in Exercises 23–64.
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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 41
In Exercises 33–68, add or subtract as indicated. 5/x + 3
Guida verificata passo dopo passo1
Identify the terms in the expression: \(\frac{5}{x} + 3\). Notice that \(\frac{5}{x}\) is a rational expression and \(3\) is a constant.
To add these terms, express the constant \(3\) as a fraction with the same denominator as \(\frac{5}{x}\). Since the denominator is \(x\), rewrite \(3\) as \(\frac{3x}{x}\).
Now the expression becomes \(\frac{5}{x} + \frac{3x}{x}\), which allows you to combine the fractions because they have a common denominator.
Add the numerators while keeping the denominator the same: \(\frac{5 + 3x}{x}\).
The simplified expression is \(\frac{5 + 3x}{x}\). This is the result of adding \(\frac{5}{x}\) and \(3\).
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Adding and Subtracting Rational Expressions
Rational expressions are fractions that contain polynomials in the numerator and denominator. To add or subtract them, you must have a common denominator. Once the denominators match, you combine the numerators accordingly and simplify the result if possible.
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Adding & Subtracting Like Radicals
Finding the Least Common Denominator (LCD)
The least common denominator is the smallest expression that both denominators can divide into without a remainder. Finding the LCD allows you to rewrite each rational expression with the same denominator, enabling addition or subtraction of the numerators.
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03:42Rationalizing Denominators Using Conjugates
Simplifying Rational Expressions
After combining rational expressions, simplifying involves factoring numerators and denominators and canceling common factors. This process reduces the expression to its simplest form, making it easier to interpret and use in further calculations.
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05:07Simplifying Algebraic Expressions
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