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Which of the following expressions is equivalent to (24)/(-12 k+84) ? Choose 1 answer: (A) (2)/(k+7) (B) (2)/(-k+7) (c) (2)/(-k+84) (D) (2)/(-12 k+7)

Which of the following expressions is equivalent to 24−12k+84 \frac{24}{-12 k+84} ?\newlineChoose 11 answer:\newline(A) 2k+7 \frac{2}{k+7} \newline(B) 2−k+7 \frac{2}{-k+7} \newline(C) 2−k+84 \frac{2}{-k+84} \newline(D) 2−12k+7 \frac{2}{-12 k+7}

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Full solution

Q. Which of the following expressions is equivalent to 24−12k+84 \frac{24}{-12 k+84} ?\newlineChoose 11 answer:\newline(A) 2k+7 \frac{2}{k+7} \newline(B) 2−k+7 \frac{2}{-k+7} \newline(C) 2−k+84 \frac{2}{-k+84} \newline(D) 2−12k+7 \frac{2}{-12 k+7}
  1. Simplify Numerator and Denominator: Simplify the numerator and denominator separately. \newline24÷−12=−224 \div -12 = -2 and 84÷−12=−784 \div -12 = -7.\newlineSo, 24−12k+84\frac{24}{-12 k+84} becomes −2k−7\frac{-2}{k-7}.
  2. Distribute Negative Sign: Notice that there's a negative sign in the numerator, which can be distributed to the denominator.\newlineSo, (−2)/(k−7)(-2)/(k-7) becomes (2)/(−k+7)(2)/(-k+7).
  3. Match with Options: Now, let's match our simplified expression with the given options.\newlineThe expression (2)/(−k+7)(2)/(-k+7) matches with option (B).

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