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Simplify the radical expression. ∛81
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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 56
In Exercises 33–68, add or subtract as indicated. 3x/(x−3) − (x+4)/(x+2)
Guida verificata passo dopo passo1
Identify the two rational expressions to be subtracted: \(\frac{3x}{x-3} - \frac{x+4}{x+2}\).
Find the least common denominator (LCD) of the two fractions, which is the product of the distinct denominators: \((x-3)(x+2)\).
Rewrite each fraction with the LCD as the new denominator by multiplying numerator and denominator accordingly: \(\frac{3x(x+2)}{(x-3)(x+2)} - \frac{(x+4)(x-3)}{(x+2)(x-3)}\).
Combine the two fractions into a single fraction by subtracting the numerators over the common denominator: \(\frac{3x(x+2) - (x+4)(x-3)}{(x-3)(x+2)}\).
Expand the numerators, simplify by combining like terms, and write the final expression as a single simplified rational expression.
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Rational Expressions
Rational expressions are fractions where the numerator and denominator are polynomials. Understanding how to manipulate these expressions, including simplifying and performing operations like addition or subtraction, is essential for solving problems involving rational expressions.
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Rationalizing Denominators
Finding a Common Denominator
To add or subtract rational expressions, you must find a common denominator, typically the least common denominator (LCD). This involves factoring denominators and determining the smallest expression that both denominators divide into, allowing the expressions to be combined.
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02:58Rationalizing Denominators
Combining and Simplifying Rational Expressions
After rewriting expressions with a common denominator, combine the numerators by addition or subtraction. Then, simplify the resulting rational expression by factoring and reducing common factors to express the answer in simplest form.
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05:07Simplifying Algebraic Expressions
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