Multiply or divide, as indicated. (m2 + 3m + 2)/(m2 + 5m + 4) ÷ (m2 + 5m + 6)/(m2 + 10m + 24)

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 43a

1장, 문제 43a

Multiply or divide, as indicated. (m² + 3m + 2)/(m² + 5m + 4) ÷ (m² + 5m + 6)/(m² + 10m + 24)

검증된 단계별 안내

Rewrite the division problem as a multiplication by taking the reciprocal of the second fraction. So, the expression becomes: \(\frac{m^2 + 3m + 2}{m^2 + 5m + 4} \times \frac{m^2 + 10m + 24}{m^2 + 5m + 6}\).

Factor each quadratic expression in the numerators and denominators. For example, factor \(m^2 + 3m + 2\), \(m^2 + 5m + 4\), \(m^2 + 5m + 6\), and \(m^2 + 10m + 24\) into products of binomials.

After factoring, rewrite the expression with all factors visible, so it looks like a product of fractions with binomial factors in numerators and denominators.

Look for common factors in the numerators and denominators across the entire expression and cancel them out to simplify the expression.

Multiply the remaining factors in the numerators together and multiply the remaining factors in the denominators together to write the simplified final expression.

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.

Factoring Quadratic Expressions

Factoring involves rewriting quadratic expressions as products of binomials. This simplifies complex rational expressions by breaking down polynomials like m² + 3m + 2 into (m + 1)(m + 2), making multiplication and division easier.

Dividing Rational Expressions

Dividing rational expressions requires multiplying by the reciprocal of the divisor. Instead of direct division, flip the second fraction and multiply, which simplifies the operation and helps in combining the expressions correctly.

Simplifying Rational Expressions

After multiplication or division, simplify the resulting expression by canceling common factors in the numerator and denominator. This reduces the expression to its simplest form, making it easier to interpret and use.