Answer x − 1 x Explanation Given: Expression: x 3 − x 2 − 4 x + 4 x 3 − 4 x Concept used: To simplify the given expression: Find the Least Common Multiple of the fraction and write in reduced form. Take out common terms in the given expression. Cancel out the terms that are in common in numerator and the denominator. Find if any algebraic identities can simplify the given expression. Calculation: Using the above concept, ⇒ x 3 − x 2 − 4 x + 4 x 3 − 4 x Consider the numerator and simplify, ⇒ x 3 − x 2 − 4 x + 4 ⇒ ( x 3 − x 2 ) − ( 4 x − 4 ) ⇒ x 2 ( x − 1 ) − 4 ( x − 1 ) ⇒ ( x 2 − 4 ) ( x − 1 ) Consider the denominator and simplify, ⇒ x 3 − 4 x ⇒ x ( x 2 − 4 ) Substituting in the numerator and denominator, ⇒ ( x 2 − 4 ) ( x − 1 ) x ( x 2 − 4 ) ⇒ ( x 2 − 4 ) ( x − 1 ) x ( x 2 − 4 ) ⇒ x − 1 x Conclusion: Therefore, the simplified form of the expression is x − 1 x .

Algebra and Trigonometry: Structure and Method, Book 2

2000th Edition

ISBN: 9780395977255

Author: MCDOUGAL LITTEL

Publisher: McDougal Littell

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Concept explainers

Percentage

A percentage is a number indicated as a fraction of 100. It is a dimensionless number often expressed using the symbol %.

Algebraic Expressions

In mathematics, an algebraic expression consists of constant(s), variable(s), and mathematical operators. It is made up of terms.

Numbers

Numbers are some measures used for counting. They can be compared one with another to know its position in the number line and determine which one is greater or lesser than the other.

Subtraction

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Before we begin to understand the addition of algebraic expressions, we need to list out a few things that form the basis of algebra.

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Question

Chapter 5.7, Problem 2ST

To determine

To simplify the given expression.

Expert Solution & Answer

Answer to Problem 2ST

x−1x

Explanation of Solution

Given:

Expression: x3−x2−4x+4x3−4x

Concept used:

To simplify the given expression:

Find the Least Common Multiple of the fraction and write in reduced form.
Take out common terms in the given expression.
Cancel out the terms that are in common in numerator and the denominator.
Find if any algebraic identities can simplify the given expression.

Calculation:

Using the above concept,

⇒x3−x2−4x+4x3−4x

Consider the numerator and simplify,

⇒x3−x2−4x+4⇒(x3−x2)−(4x−4)⇒x2(x−1)−4(x−1)⇒(x2−4)(x−1)

Consider the denominator and simplify,

⇒x3−4x⇒x(x2−4)

Substituting in the numerator and denominator,

⇒(x2−4)(x−1)x(x2−4)⇒(x2−4)(x−1)x(x2−4)⇒x−1x

Conclusion:

Therefore, the simplified form of the expression is x−1x.

Chapter 5.7, Problem 1ST

Chapter 5.7, Problem 3ST

Chapter 5 Solutions

Algebra and Trigonometry: Structure and Method, Book 2

Ch. 5.1 - Prob. 1OE Ch. 5.1 - Prob. 2OE Ch. 5.1 - Prob. 3OE Ch. 5.1 - Prob. 4OE Ch. 5.1 - Prob. 5OE Ch. 5.1 - Prob. 6OE Ch. 5.1 - Prob. 7OE Ch. 5.1 - Prob. 8OE Ch. 5.1 - Prob. 9OE Ch. 5.1 - Prob. 10OE

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