Solve each equation. See Example 2. (4x+3)/(x+1) + 2/x = 1/(x2+x)

Ch. 1 - Equations and Inequalities

Lial13th EditionCollege AlgebraISBN: 9780136881063당신이 사용하는 게 아니라요?교과서 변경

모든 교과서

Lial 13th Edition

Ch. 1 - Equations and Inequalities

문제 26

2장, 문제 26

Solve each equation. See Example 2. (4x+3)/(x+1) + 2/x = 1/(x²+x)

검증된 단계별 안내

Identify the given equation: \(\frac{4x+3}{x+1} + \frac{2}{x} = \frac{1}{x^{2} + x}\).

Recognize that the denominator on the right side, \(x^{2} + x\), can be factored as \(x(x+1)\).

Find the least common denominator (LCD) for all terms, which is \(x(x+1)\).

Multiply every term in the equation by the LCD \(x(x+1)\) to eliminate the denominators.

After clearing denominators, simplify the resulting equation and solve the resulting polynomial equation for \(x\).

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.

Rational Expressions

Rational expressions are fractions where the numerator and denominator are polynomials. Understanding how to manipulate these expressions, including simplifying and finding common denominators, is essential for solving equations involving rational terms.

Least Common Denominator (LCD)

The least common denominator is the smallest expression that all denominators in a rational equation can divide into evenly. Identifying the LCD allows you to combine or clear fractions by multiplying through, simplifying the equation to a polynomial form.

Solving Rational Equations

Solving rational equations involves eliminating denominators by multiplying both sides by the LCD, then solving the resulting polynomial equation. It's important to check for extraneous solutions that make any denominator zero, as these are not valid.