Simplify each complex fraction. m−1m2−41m+2\frac{m - \frac{1}{$$m^2 - 4$$}}{\frac{1}{m + 2}} m+21m−m2−41

Ch. R - Review of Basic Concepts

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Lial 13th Edition

Ch. R - Review of Basic Concepts

문제 79

1장, 문제 79

Simplify each complex fraction. $$\frac{m - \frac{1}{m^2 - 4}$}{$\frac{1}{m + 2}$}$

검증된 단계별 안내

Identify the complex fraction: the numerator is $m - \frac{1}{m^{2} - 4}$ and the denominator is $\frac{1}{m + 2}$.

Recognize that $m^{2} - 4$ is a difference of squares and factor it as $(m - 2)(m + 2)$.

Rewrite the numerator as $m - \frac{1}{(m - 2)(m + 2)}$ to have a common denominator for the terms in the numerator.

Express $m$ as $\frac{m(m - 2)(m + 2)}{(m - 2)(m + 2)}$ so that both terms in the numerator share the denominator $(m - 2)(m + 2)$, then combine them into a single fraction.

Divide the resulting numerator fraction by the denominator $\frac{1}{m + 2}$ by multiplying the numerator fraction by the reciprocal of the denominator, which is $(m + 2)$.

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주요 개념

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

Complex Fractions

A complex fraction is a fraction where the numerator, denominator, or both contain fractions themselves. Simplifying involves rewriting the expression as a single fraction by finding common denominators or multiplying by the reciprocal of the denominator.

Factoring Quadratic Expressions

Factoring involves expressing a quadratic expression as a product of simpler binomials. For example, m^2 - 4 is a difference of squares and factors into (m - 2)(m + 2), which helps simplify fractions by canceling common factors.

Multiplying by the Reciprocal

To divide by a fraction, multiply by its reciprocal. In this problem, dividing by 1/(m + 2) is equivalent to multiplying by (m + 2), which simplifies the complex fraction into a simpler algebraic expression.

Simplify each complex fraction. m−1m2−41m+2\(\frac{m - \frac{1}{m^2 - 4}\)}{\(\frac{1}{m + 2}\)} m+21m−m2−41

비슷한 문제에 대한 검증된 영상 답변:

주요 개념

Complex Fractions

Factoring Quadratic Expressions

Multiplying by the Reciprocal

Simplify each complex fraction. $\(\frac{m - \frac{1}{m^2 - 4}\)}{\(\frac{1}{m + 2}\)}$