Skip to main content
Ch. P - Fundamental Concepts of Algebra
Blitzer - College Algebra 8th Edition
Blitzer8th EditionCollege AlgebraISBN: 9780136970514당신이 사용하는 게 아니라요?교과서 변경
모든 교과서Blitzer 8th EditionCh. P - Fundamental Concepts of Algebra문제 99
1장, 문제 99

In Exercises 93–102, factor and simplify each algebraic expression. (x+5)−1/2−(x+5)−3/2

검증된 단계별 안내
1
Rewrite the expression using a common base. Both terms involve the base (x + 5) raised to different exponents. Let’s rewrite the expression as: (x + 5)^(-1/2) - (x + 5)^(-3/2).
Factor out the smallest power of (x + 5) from both terms. The smallest power here is (x + 5)^(-3/2). Factoring this out gives: (x + 5)^(-3/2) * [(x + 5)^(1) - 1].
Simplify the term inside the brackets. The expression becomes: (x + 5)^(-3/2) * [(x + 5) - 1].
Combine the terms inside the brackets. Simplify (x + 5) - 1 to get x + 4. The expression now becomes: (x + 5)^(-3/2) * (x + 4).
Express the final result in simplified form. The factored and simplified expression is: (x + 4) / (x + 5)^(3/2).

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.
영상 길이:
3m
도움이 되었나요?

주요 개념

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

Exponents and Negative Exponents

Exponents represent repeated multiplication of a base number. A negative exponent indicates the reciprocal of the base raised to the absolute value of the exponent. For example, a^(-n) = 1/(a^n). Understanding how to manipulate negative exponents is crucial for simplifying expressions like (x+5)^(-1/2) and (x+5)^(-3/2).
추천 영상:
04:06
Rational Exponents

Factoring Algebraic Expressions

Factoring involves rewriting an expression as a product of its factors. This process is essential for simplifying complex algebraic expressions. In the given expression, recognizing common factors can help in reducing the terms effectively, making it easier to simplify the overall expression.
추천 영상:
05:09
Introduction to Algebraic Expressions

Simplifying Algebraic Fractions

Simplifying algebraic fractions involves reducing the fraction to its simplest form by canceling common factors in the numerator and denominator. This process often requires factoring and understanding the properties of exponents. In the context of the given expression, simplifying will lead to a clearer and more manageable form.
추천 영상:
05:07
Simplifying Algebraic Expressions
관련 실천
교과서 질문

In Exercises 91–100, simplify using properties of exponents. (3y1/4)3/y1/12

166
views
교과서 질문

In Exercises 97–102, write each algebraic expression without parentheses. 1/3(3x)+[(4y)+(−4y)]

168
views
교과서 질문
In Exercises 87–106, perform the indicated computations. Write the answers in scientific notation. If necessary, round the decimal factor in your scientific notation answer to two decimal places. (2.4×10^−2)/(4.8×10^-6)
846
views
교과서 질문

In Exercises 93–102, factor and simplify each algebraic expression. (x+3)1/2−(x+3)3/2

131
views
교과서 질문

Factor completely, or state that the polynomial is prime. 16x^2-40x+25

254
views
교과서 질문
In Exercises 87–106, perform the indicated computations. Write the answers in scientific notation. If necessary, round the decimal factor in your scientific notation answer to two decimal places. (1.2×10^4)/(2×10^−2)
820
views