Add or subtract, as indicated. 1/a + b/a2

Ch. R - Review of Basic Concepts

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Lial 13th Edition

Ch. R - Review of Basic Concepts

문제 55a

1장, 문제 55a

Add or subtract, as indicated. 1/a + b/a²

검증된 단계별 안내

Identify the terms to be added: \(\frac{1}{a}\) and \(\frac{b}{a^2}\).

Find a common denominator for the fractions. Since the denominators are \(a\) and \(a^2\), the least common denominator (LCD) is \(a^2\).

Rewrite each fraction with the common denominator \(a^2\): multiply the numerator and denominator of \(\frac{1}{a}\) by \(a\) to get \(\frac{a}{a^2}\), and keep \(\frac{b}{a^2}\) as is.

Add the numerators over the common denominator: \(\frac{a}{a^2} + \frac{b}{a^2} = \frac{a + b}{a^2}\).

Express the final answer as a single fraction: \(\frac{a + b}{a^2}\).

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주요 개념

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

Like and Unlike Denominators

When adding or subtracting fractions, the denominators must be the same. Fractions with different denominators are called unlike fractions and require finding a common denominator before performing the operation.

Finding the Least Common Denominator (LCD)

The least common denominator is the smallest expression that both denominators divide into evenly. For algebraic fractions, the LCD is found by factoring denominators and taking the highest powers of each factor.

Adding Fractions with Algebraic Expressions

After rewriting fractions with the LCD, add or subtract the numerators while keeping the common denominator. Simplify the resulting expression by combining like terms and reducing if possible.