Which expression is equivalent to (8x(x−7)−3(x−7))/(2x−14), where x > 7?
Correct answer: B (parsed from the explanation — this source omits an answer key for this item)
Explanation
Choice B is correct. The given expression has a common factor of 2 in the 8 -7-3 -7 denominator, so the expression can be rewritten as x^x 2 h -7^x h. The three ^x h - terms in this expression have a common factor of ^x 7h. Since it’s given that > - x 7, x can’t be equal to 7, which means ^x 7h can’t be equal to 0. Therefore, each term in the expression, 8 x^x - 2 7 h - - 3 7^x -7 h, can be divided by ^x - 7h, which 8 -3 ^x h gives x2 . Choice A is incorrect and may result from conceptual or calculation errors. Choice C is incorrect and may result from conceptual or calculation errors. Choice D is incorrect and may result from conceptual or calculation errors.
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