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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 3
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In Exercises 1–6, find all numbers that must be excluded from the domain of each rational expression. (x+5)/(x2−25)

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Identify the domain of a rational expression. The domain includes all real numbers except those that make the denominator equal to zero, as division by zero is undefined.
Write the denominator of the given rational expression: x^2 - 25.
Set the denominator equal to zero to find the values that must be excluded: x^2 - 25 = 0.
Factor the denominator using the difference of squares formula: x^2 - 25 = (x - 5)(x + 5).
Solve for the values of x that make the denominator zero: x - 5 = 0 gives x = 5, and x + 5 = 0 gives x = -5. These are the values that must be excluded from the domain.

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주요 개념

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

Rational Expressions

A rational expression is a fraction where both the numerator and the denominator are polynomials. Understanding rational expressions is crucial because they can have restrictions on their domain, specifically where the denominator equals zero, as division by zero is undefined.
추천 영상:
02:58
Rationalizing Denominators

Domain of a Function

The domain of a function refers to the set of all possible input values (x-values) for which the function is defined. For rational expressions, the domain excludes any values that make the denominator zero, as these values would lead to undefined expressions.
추천 영상:
3:51
Domain Restrictions of Composed Functions

Factoring Polynomials

Factoring polynomials involves breaking down a polynomial into simpler components (factors) that, when multiplied together, yield the original polynomial. This is essential for identifying values that make the denominator zero, allowing us to determine which numbers must be excluded from the domain.
추천 영상:
07:30
Introduction to Factoring Polynomials
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