Textbook Question
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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Table of contents
- 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
Chapter 1, Problem 11
In Exercises 1–16, evaluate each algebraic expression for the given value or values of the variable(s). x2-3(x-y), for x=8 and y=2
Verified step by step guidance1
Step 1: Start by substituting the given values of the variables into the algebraic expression. Replace x with 8 and y with 2 in the expression x^2 - 3(x - y).
Step 2: Rewrite the expression after substitution: (8)^2 - 3(8 - 2).
Step 3: Simplify the exponentiation first. Calculate 8^2, which means multiplying 8 by itself.
Step 4: Simplify the parentheses next. Subtract 2 from 8 to evaluate (8 - 2).
Step 5: Multiply the result of (8 - 2) by -3, then combine it with the result of 8^2 to simplify the entire expression.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Algebraic Expressions
An algebraic expression is a mathematical phrase that can include numbers, variables, and operation symbols. In this case, the expression x^2 - 3(x - y) combines these elements to represent a value based on the variables x and y. Understanding how to manipulate and evaluate these expressions is fundamental in algebra.
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Substitution
Substitution is the process of replacing variables in an expression with their corresponding numerical values. For the given expression, substituting x = 8 and y = 2 means replacing x and y in the expression to simplify and calculate the result. This technique is essential for evaluating algebraic expressions accurately.
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Order of Operations
The order of operations is a set of rules that dictates the sequence in which different operations should be performed in a mathematical expression. Commonly remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction), following this order ensures that calculations are performed correctly and consistently.
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Related Practice
Textbook Question
Evaluate each exponential expression in Exercises 1–22. 4−3
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Textbook Question
In Exercises 11–16, factor by grouping. x3−3x2+4x−12
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Textbook Question
Rewrite each expression without the absolute value bars. |√2-1|
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Textbook Question
Evaluate each expression in Exercises 1–12, or indicate that the root is not a real number.
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Textbook Question
In Exercises 9–14, perform the indicated operations. Write the resulting polynomial in standard form and indicate its degree. (17x3−5x2+4x−3)−(5x3−9x2−8x+11)
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