Add or subtract as indicated. (4x−10)/(x−2) − (x−4)/(x−2)

검증된 단계별 안내

Identify that both rational expressions have the same denominator, which is \(x - 2\).

Since the denominators are the same, combine the numerators by subtracting: \((4x - 10) - (x - 4)\).

Distribute the subtraction across the second numerator: \(4x - 10 - x + 4\).

Combine like terms in the numerator: \((4x - x) + (-10 + 4)\).

Write the simplified numerator over the common denominator: \(\frac{3x - 6}{x - 2}\).

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.

Like Denominators in Rational Expressions

When adding or subtracting rational expressions, the denominators must be the same. If the denominators are identical, you can combine the numerators directly while keeping the denominator unchanged. This simplifies the process and avoids the need for finding a common denominator.

Combining Numerators

After confirming the denominators are the same, subtract or add the numerators as indicated. This involves combining like terms carefully to simplify the resulting expression. Proper handling of subtraction signs is crucial to avoid errors.

Simplifying Rational Expressions

Once the numerators are combined, simplify the resulting rational expression by factoring and reducing common factors if possible. Simplification makes the expression easier to interpret and use in further calculations.