Add or subtract, as indicated. 4/x + 1 + 1/x2 - x + 1 - 12/x3 + 1

Ch. R - Review of Basic Concepts

Lial13th EditionCollege AlgebraISBN: 9780136881063당신이 사용하는 게 아니라요?교과서 변경

모든 교과서

Lial 13th Edition

Ch. R - Review of Basic Concepts

문제 67a

1장, 문제 67a

Add or subtract, as indicated. 4/x + 1 + 1/x² - x + 1 - 12/x³ + 1

검증된 단계별 안내

Identify and group like terms based on their powers of \(x\). The terms are: \(\frac{4}{x}\), \(1\), \(\frac{1}{x^2}\), \(-x\), \(1\), \(-\frac{12}{x^3}\), and \(1\).

Combine the constant terms: \(1 + 1 + 1\).

Write the expression grouping terms by powers of \(x\): \(-\frac{12}{x^3} + \frac{1}{x^2} + \frac{4}{x} - x + (1 + 1 + 1)\).

Since the terms have different powers of \(x\), the expression cannot be simplified further by combining unlike terms; just write the simplified constants and keep the rest as is.

Present the final simplified expression as a sum of terms with constants combined and other terms in their fractional or polynomial form.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

도움이 되었나요?

주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Combining Like Terms

Combining like terms involves adding or subtracting terms that have the same variable raised to the same power. This simplifies expressions by reducing the number of terms. For example, terms with x² can be combined, but terms with x and x² cannot.

Operations with Rational Expressions

Rational expressions are fractions that contain polynomials in the numerator, denominator, or both. Adding or subtracting them requires a common denominator. Once the denominators match, you combine the numerators accordingly.

Polynomial Arithmetic

Polynomial arithmetic includes adding, subtracting, and multiplying polynomials by combining like terms and applying distributive properties. Understanding how to manipulate polynomials is essential when simplifying expressions involving multiple terms with variables.