Domanda del libro di testo
Use the quotient rule to simplify the expressions in Exercises 45-46. √(121/4)
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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 44
In Exercises 33–68, add or subtract as indicated. 3x/8 + x/12
Guida verificata passo dopo passo1
Identify the least common denominator (LCD) of the fractions. The denominators are 8 and 12. The LCD is the smallest number that both 8 and 12 divide into evenly. In this case, the LCD is 24.
Rewrite each fraction with the LCD as the denominator. To do this, multiply both the numerator and denominator of each fraction by the factor needed to make the denominator equal to 24. For \( \frac{3x}{8} \), multiply by \( \frac{3}{3} \), and for \( \frac{x}{12} \), multiply by \( \frac{2}{2} \).
After rewriting, the fractions become \( \frac{9x}{24} \) and \( \frac{2x}{24} \).
Since the denominators are now the same, you can add the numerators directly. Combine \( 9x \) and \( 2x \) to get \( 11x \).
Write the result as a single fraction: \( \frac{11x}{24} \). This is the simplified form of the sum.
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Finding a Common Denominator
To add or subtract fractions, it is essential to find a common denominator. The common denominator is the least common multiple (LCM) of the denominators involved. In this case, the denominators are 8 and 12, and the LCM is 24. This allows us to rewrite each fraction with the same denominator, making it possible to combine them.
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Rationalizing Denominators
Fraction Addition
Fraction addition involves combining two or more fractions into a single fraction. Once the fractions have a common denominator, you can add the numerators while keeping the common denominator the same. For example, if we convert 3x/8 and x/12 to have a denominator of 24, we can then add the adjusted numerators to find the sum.
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05:45Radical Expressions with Fractions
Simplifying Fractions
After performing operations on fractions, it is often necessary to simplify the result. Simplifying a fraction involves dividing both the numerator and the denominator by their greatest common divisor (GCD). This process ensures that the fraction is expressed in its simplest form, making it easier to understand and work with.
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05:45Radical Expressions with Fractions
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