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Advanced Math / Equivalent expressions Difficulty: Medium

The expression $\frac{24}{6 x + 42}$ is equivalent to $\frac{4}{x + b}$ , where b is a constant and $x greater than 0$ . What is the value of b?

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Explanation

Choice A is correct. Since the given expressions are equivalent and the numerator of the second expression is $\frac{1}{6}$ of the numerator of the first expression, the denominator of the second expression must also be $\frac{1}{6}$ of the denominator of the first expression. By the distributive property, $one sixth left parenthesis 6 x plus 42 right parenthesis$ is equivalent to $one sixth left parenthesis 6 x right parenthesis plus one sixth left parenthesis 42 right parenthesis$ , or $x plus 7$ . Therefore, the value of $b$ is $7$ .

Choice B 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.