## Precalculus (6th Edition)

$\color{blue}{\dfrac{-7\sqrt3}{36}}$
Simplify the denominators to obtain: $=\dfrac{2}{\sqrt{4(3)}} - \dfrac{1}{\sqrt{9(3)}} - \dfrac{5}{\sqrt{16(3)}} \\=\dfrac{2}{2\sqrt3} - \dfrac{1}{3\sqrt{3}}- \dfrac{5}{4\sqrt{3}} \\=\dfrac{1}{\sqrt3} - \dfrac{1}{3\sqrt{3}}- \dfrac{5}{4\sqrt{3}}$ Make the expressions similar by using their LCD of $12\sqrt{3}$ to obtain: $=\dfrac{1(12)}{\sqrt3(12)}- \dfrac{1(4)}{3\sqrt3(4)}-\dfrac{5(3)}{4\sqrt{3}(3)} \\=\dfrac{12}{12\sqrt3}-\dfrac{4}{12\sqrt3}-\dfrac{15}{12\sqrt3}$ Subtract the second and third numerators to the first and copy the denominator to obtain: $=\dfrac{12-4-15}{12\sqrt3} \\=\dfrac{-7}{12\sqrt3}$ Rationalize the denominator by multiplying $\sqrt3$ to both the numerator and the denominator to obtain: $=\dfrac{-7(\sqrt3)}{12\sqrt3(\sqrt3)} \\=\dfrac{-7\sqrt3}{12(3)} \\=\color{blue}{\dfrac{-7\sqrt3}{36}}$
The text passage contains a mathematical problem involving the simplification of a given expression, and the solution to the problem is provided step-by-step, leading to the final answer.
single_question_with_answer
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
## Precalculus (6th Edition)

$\color{blue}{\dfrac{-7\sqrt3}{36}}$
Simplify the denominators to obtain: $=\dfrac{2}{\sqrt{4(3)}} - \dfrac{1}{\sqrt{9(3)}} - \dfrac{5}{\sqrt{16(3)}} \\=\dfrac{2}{2\sqrt3} - \dfrac{1}{3\sqrt{3}}- \dfrac{5}{4\sqrt{3}} \\=\dfrac{1}{\sqrt3} - \dfrac{1}{3\sqrt{3}}- \dfrac{5}{4\sqrt{3}}$ Make the expressions similar by using their LCD of $12\sqrt{3}$ to obtain: $=\dfrac{1(12)}{\sqrt3(12)}- \dfrac{1(4)}{3\sqrt3(4)}-\dfrac{5(3)}{4\sqrt{3}(3)} \\=\dfrac{12}{12\sqrt3}-\dfrac{4}{12\sqrt3}-\dfrac{15}{12\sqrt3}$ Subtract the second and third numerators to the first and copy the denominator to obtain: $=\dfrac{12-4-15}{12\sqrt3} \\=\dfrac{-7}{12\sqrt3}$ Rationalize the denominator by multiplying $\sqrt3$ to both the numerator and the denominator to obtain: $=\dfrac{-7(\sqrt3)}{12\sqrt3(\sqrt3)} \\=\dfrac{-7\sqrt3}{12(3)} \\=\color{blue}{\dfrac{-7\sqrt3}{36}}$
user
The text passage contains a mathematical problem involving the simplification of a given expression, and the solution to the problem is provided step-by-step, leading to the final answer.

TYPE: SINGLE_QUESTION_WITH_ANSWER