1. **State the problem:** Simplify the expression $$\frac{6 + \frac{1}{x}}{5 - \frac{1}{x}}$$ and find values of $x$ for which the expression is undefined. 2. **Rewrite the expression:** To simplify, multiply numerator and denominator by $x$ to clear the fractions: $$\frac{6 + \frac{1}{x}}{5 - \frac{1}{x}} = \frac{(6 + \frac{1}{x}) \cdot x}{(5 - \frac{1}{x}) \cdot x}$$ 3. **Multiply out:** $$= \frac{6x + 1}{5x - 1}$$ 4. **Simplify:** The expression is now $$\frac{6x + 1}{5x - 1}$$ which cannot be simplified further. 5. **Find values where expression is undefined:** The denominator cannot be zero, so solve: $$5x - 1 = 0 \implies x = \frac{1}{5}$$ 6. **Also consider original restrictions:** Since the original expression has $\frac{1}{x}$, $x \neq 0$. 7. **Final answer:** $$\frac{6 + \frac{1}{x}}{5 - \frac{1}{x}} = \frac{6x + 1}{5x - 1}$$ with restrictions $$x \neq 0, x \neq \frac{1}{5}$$