\( \left\lvert\, \begin{array}{cc}\text { Divide. Write the answer in simplest form. } \\ \begin{array}{cc}\frac{6}{7}+36 \\ 0 & 1 / 14 \\ 0 & 1 / 21 \\ 0 & 1 / 42\end{array}\end{array}\right. \)

To divide \( \frac{6}{7} + 36 \), we first need to convert 36 into a fraction. That would be \( \frac{36}{1} \). Now, to add these fractions, we must make a common denominator. The least common multiple of 7 and 1 is 7. Thus, the conversion gives us: \[ \frac{6}{7} + \frac{36 \times 7}{1 \times 7} = \frac{6}{7} + \frac{252}{7} = \frac{6 + 252}{7} = \frac{258}{7}. \] Now, let's look at the answer in its simplest form. The greatest common divisor (GCD) for 258 and 7 is 1, so \( \frac{258}{7} \) is already simplified. Now, examining the other values provided, the simplest form of: - \( \frac{1}{14} \) is unique, cannot be simplified further. - \( \frac{1}{21} \) is also in its simplest form. - \( \frac{1}{42} \) also can't go lower. So, your final answer is \( \frac{258}{7} \). Exciting, isn't it? Fractions hold secrets waiting to be simplified!