Multiply or divide, as indicated. See Example 3. ((x² + x) / 5) • 25 / (xy + y)

검증된 단계별 안내

First, rewrite the given expression clearly as a multiplication of two fractions: \(\frac{x^2 + x}{5xy} \times \frac{25}{y}\).

Next, factor any expressions where possible. For example, factor \(x^2 + x\) as \(x(x + 1)\).

Rewrite the expression with the factored form: \(\frac{x(x + 1)}{5xy} \times \frac{25}{y}\).

Multiply the numerators together and the denominators together: \(\frac{x(x + 1) \times 25}{5xy \times y}\).

Simplify the resulting fraction by canceling common factors in numerator and denominator, such as \(x\) and any numerical factors.

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주요 개념

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

Algebraic Expression Simplification

Simplifying algebraic expressions involves combining like terms, factoring polynomials, and reducing fractions. This process makes complex expressions easier to work with, especially before performing multiplication or division.

Multiplication and Division of Rational Expressions

When multiplying or dividing rational expressions, factor all numerators and denominators first, then cancel common factors. Division requires multiplying by the reciprocal of the divisor to simplify the expression correctly.

Factoring Polynomials

Factoring breaks down polynomials into products of simpler polynomials or terms. Recognizing common factoring techniques, such as factoring out the greatest common factor or using special products, is essential for simplifying and manipulating expressions.