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Equivalent expressions SAT question

Math · Advanced Math · Medium · Answer it here, explanation included.

Which expression is equivalent to $\frac{8 x ( x - 7 ) - 3 ( x - 7 )}{2 x - 14}$ , where $x > 7$ ?

ExplanationShow

Choice B is correct. The given expression has a common factor of $2$ in the denominator, so the expression can be rewritten as $\frac{8 x ( x - 7 ) - 3 ( x - 7 )}{2 ( x - 7 )}$ . The three terms in this expression have a common factor of $(x - 7)$ . Since it's given that $x > 7$ , $x$ can't be equal to $7$ , which means $(x - 7)$ can't be equal to $0$ . Therefore, each term in the expression, $\frac{8 x ( x - 7 ) - 3 ( x - 7 )}{2 ( x - 7 )}$ , can be divided by $(x - 7)$ , which gives $\frac{8 x - 3}{2}$ .

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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Equivalent expressions SAT question

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