Which expression is equivalent to 4 ⁄ 4x − 5 − 1 ⁄ x + 1 ?

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Accepted Answer

Key Explanation: Choice A is correct. To subtract one rational expression from another, the denominators of the expressions must be the same. Since 4x − 5 and x + 1 do not have any common factors, each rational expression should be rewritten with a denominator of (x + 1)(4x − 5). Multiplying 4 ⁄ 4x − 5 by x + 1 ⁄ x + 1 and multiplying 1 ⁄ x + 1 by 4x − 5 ⁄ 4x − 5 yields 4(x + 1) ⁄ (x + 1)(4x − 5) − 4x − 5 ⁄ (x + 1)(4x − 5) . This expression can be rewritten using the distributive property, which yields 4x + 4 ⁄ (x + 1)(4x − 5) − 4x − 5 ⁄ (x + 1)(4x − 5) . Since the denominators are the same, this expression is equivalent to 4x + 4 − 4x + 5 ⁄ (x + 1)(4x − 5) , or 9 ⁄ (x + 1)(4x − 5) . Distractor Explanations: Choices B, C, and D are incorrect and may result from conceptual or calculation errors.

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