Question

Solve: \( 3 + \frac{1}{2 + \frac{1}{5 + \frac{1}{4}}} \)

• A. \( \frac{159}{46} \)
• B. \( \frac{157}{42} \)
• C. \( \frac{147}{39} \)
• D. \( \frac{151}{42} \)

Hint:

When simplifying complex fractions, always start with the innermost fraction and work outward.

Answer 1

The Correct Option is A

We need to simplify the given expression step by step: \[ 3 + \frac{1}{2 + \frac{1}{5 + \frac{1}{4}}} \] Step 1: Start from the innermost fraction. \[ 5 + \frac{1}{4} = \frac{20}{4} + \frac{1}{4} = \frac{21}{4} \]

Step 2: Substitute this into the next fraction. \[ 2 + \frac{1}{\frac{21}{4}} = 2 + \frac{4}{21} = \frac{42}{21} + \frac{4}{21} = \frac{46}{21} \]

Step 3: Now substitute this back into the original expression. \[ 3 + \frac{1}{\frac{46}{21}} = 3 + \frac{21}{46} = \frac{138}{46} + \frac{21}{46} = \frac{159}{46} \] Thus, the simplified answer is \( \frac{159}{46} \).