Multiply or divide as indicated. x3−8x2−4⋅x+23x\frac{$$x^3 - 8$$}{$$x^2 - 4$$} \cdot \frac{x + 2}{3x} x2−4x3−8⋅3xx+2

Ch. P - Fundamental Concepts of Algebra

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Blitzer 8th Edition

Ch. P - Fundamental Concepts of Algebra

문제 21

1장, 문제 21

Multiply or divide as indicated. $\frac{x^3 - 8}{x^2 - 4}\) $\cdot$ \(\frac{x + 2}{3x}$

검증된 단계별 안내

Identify the given expression to multiply: $\frac{\left(x^3 - 8\right)}{\left(x^2 - 4\right)} \cdot \frac{\left(x + 2\right)}{3x}$.

Factor all polynomials where possible. Recognize that $x^3 - 8$ is a difference of cubes and $x^2 - 4$ is a difference of squares. Use the formulas: $a^3 - b^3 = (a - b)(a^2 + ab + b^2)$ and $a^2 - b^2 = (a - b)(a + b)$.

Rewrite the expression with factored forms: $\frac{(x - 2)(x^2 + 2x + 4)}{(x - 2)(x + 2)} \cdot \frac{(x + 2)}{3x}$.

Cancel out common factors in the numerator and denominator, such as $(x - 2)$ and $(x + 2)$, to simplify the expression.

Multiply the remaining factors in the numerator and denominator to write the simplified expression as a single fraction.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

주요 개념

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

Polynomial Factoring

Factoring polynomials involves rewriting expressions as products of simpler polynomials. Recognizing special forms like difference of cubes (x³ - 8) and difference of squares (x² - 4) helps simplify expressions before multiplication or division.

Multiplication and Division of Rational Expressions

When multiplying or dividing rational expressions, factor all numerators and denominators first, then multiply across numerators and denominators. For division, multiply by the reciprocal of the divisor to simplify the expression.

Simplifying Rational Expressions

Simplifying involves canceling common factors in the numerator and denominator after factoring. This reduces the expression to its simplest form, making it easier to interpret or use in further calculations.

Multiply or divide as indicated. x3−8x2−4⋅x+23x\(\frac{x^3 - 8}{x^2 - 4}\) \(\cdot\) \(\frac{x + 2}{3x}\) x2−4x3−8⋅3xx+2

비슷한 문제에 대한 검증된 영상 답변:

주요 개념

Polynomial Factoring

Multiplication and Division of Rational Expressions

Simplifying Rational Expressions

Multiply or divide as indicated. $\frac{x^3 - 8}{x^2 - 4}\) \(\cdot\) \(\frac{x + 2}{3x}$