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Find each product. (x−1)(x+2)
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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 24
Multiply or divide as indicated.
Guida verificata passo dopo passo1
Rewrite the division of fractions as multiplication by the reciprocal. So, \( \frac{(x+5)}{7} \div \frac{(4x+20)}{9} \) becomes \( \frac{(x+5)}{7} \times \frac{9}{(4x+20)} \).
Factor any expressions that can be simplified. Notice that \(4x + 20\) can be factored as \(4(x + 5)\).
Substitute the factored form back into the expression: \( \frac{(x+5)}{7} \times \frac{9}{4(x+5)} \).
Cancel out the common factor \( (x+5) \) from numerator and denominator, assuming \(x \neq -5\) to avoid division by zero.
Multiply the remaining numerators and denominators: \( \frac{1 \times 9}{7 \times 4} \) to get the simplified expression.
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Division of Rational Expressions
Dividing rational expressions involves multiplying the first expression by the reciprocal of the second. Instead of directly dividing, you flip the numerator and denominator of the divisor and then multiply, simplifying the process.
Video consigliato:
02:58
Rationalizing Denominators
Factoring Polynomials
Factoring polynomials means rewriting them as a product of simpler expressions. For example, 4x + 20 can be factored as 4(x + 5), which helps in simplifying rational expressions by canceling common factors.
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07:30Introduction to Factoring Polynomials
Simplifying Rational Expressions
Simplifying rational expressions involves reducing them to their simplest form by canceling common factors in the numerator and denominator. This makes the expression easier to work with and understand.
Video consigliato:
05:07Simplifying Algebraic Expressions
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