In Exercises 33–68, add or subtract as indicated. 5/x + 3

검증된 단계별 안내

Identify the terms in the expression: \(\frac{5}{x} + 3\). Notice that \(\frac{5}{x}\) is a rational expression and \(3\) is a constant.

To add these terms, express the constant \(3\) as a fraction with the same denominator as \(\frac{5}{x}\). Since the denominator is \(x\), rewrite \(3\) as \(\frac{3x}{x}\).

Now the expression becomes \(\frac{5}{x} + \frac{3x}{x}\), which allows you to combine the fractions because they have a common denominator.

Add the numerators while keeping the denominator the same: \(\frac{5 + 3x}{x}\).

The simplified expression is \(\frac{5 + 3x}{x}\). This is the result of adding \(\frac{5}{x}\) and \(3\).

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이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

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주요 개념

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

Adding and Subtracting Rational Expressions

Rational expressions are fractions that contain polynomials in the numerator and denominator. To add or subtract them, you must have a common denominator. Once the denominators match, you combine the numerators accordingly and simplify the result if possible.

Finding the Least Common Denominator (LCD)

The least common denominator is the smallest expression that both denominators can divide into without a remainder. Finding the LCD allows you to rewrite each rational expression with the same denominator, enabling addition or subtraction of the numerators.

Simplifying Rational Expressions

After combining rational expressions, simplifying involves factoring numerators and denominators and canceling common factors. This process reduces the expression to its simplest form, making it easier to interpret and use in further calculations.