It looks like you're trying to express a mathematical equation or expression. However, the formatting seems a bit unclear. Let's rewrite it step-by-step and simplify it.

Your expression appears to be:

\[
\frac{1}{2}x + 1 - \frac{1}{x} + 3 + \frac{5x}{2x} + \frac{61}{2}x + 1 - \frac{1}{x} + 3 + \frac{5x}{2x} + 6
\]

To simplify, we can combine like terms and perform any necessary operations. Let's break it down:

1. Rearranging terms:
- \( \frac{1}{2}x + \frac{61}{2}x + \frac{5x}{2x} + \frac{5x}{2x} + 1 + 1 + 3 + 3 + 6 - \frac{1}{x} - \frac{1}{x} \)

2. Combine the constant terms:
- \( 1 + 1 + 3 + 3 + 6 = 14 \)

3. The \( x \) terms combined:
- Calculate \( \frac{1}{2}x \) and \( \frac{61}{2}x \):
- \( \frac{1}{2}x + \frac{61}{2}x = \frac{62}{2}x = 31x \)

4. The \( \frac{5x}{2x} \) term cancels out (it simplifies to \( \frac{5}{2} \) since \( x/x = 1 \)).
- So including two of those terms gives us \( 2 \cdot \frac{5}{2} = 5 \).

5. Now we can combine all terms:
- Total \( x \) terms: \( 31x + 5 \)
- The constants: \( 14 \)
- Combining: \( 31x + 5 + 14 - 2 \cdot \frac{1}{x} \)
- So we have: \( 31x + 19 - \frac{2}{x} \)

Putting it all together, the simplified expression would be:

\[
31x + 19 - \frac{2}{x}
\]

If this format or simplification is not what you intended, please provide clear details, and I'd be happy to help with that!