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Chapter 14: Problem 6

\(k>0\) \(l>1\) Quantity A \(\frac{1}{\frac{1}{k}+\frac{1}{l}}\) Quantity B \(\frac{k l}{\frac{1}{k}+\frac{1}{l}}\) a. Quantity A is greater. b. Quantity B is greater. c. The two quantities are equal. d. The relationship cannot be determined from the information given.

Short Answer

Expert verified
The correct answer is (c). The two quantities are equal.

Step by step solution

01

Simplify Quantity A

Start by simplifying Quantity A formula. Note that the two fractions are in the denominator of a larger fraction. Therefore, to simplify, add the fractions in the denominator to get \(\frac{1}{\frac{k+l}{kl}}\). Then divide the numerator by the denominator to simplify the fraction further to \(\frac{kl}{k+l}\).
02

Simplify Quantity B

For Quantity B, notice that it has the same denominator as Quantity A after simplification. Therefore, Quantity B is actually \(\frac{kl}{k+l}\), which is equal to Quantity A.
03

Compare the Quantities

Now that both quantities have been simplified to the same expression, it is clear that Quantity A = Quantity B. This is true irrespective of the values of k and l as long as k>0 and l>1 (which ensures our denominators are never zero).

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