Rational Function 4477D1

1. **Problem statement:** We are given the function $$y = \frac{x+5}{-x+2}$$ and asked to analyze or simplify it. 2. **Rewrite the function:** Notice that $$-x+2$$ can be rewritten as $$2 - x$$, so the function is equivalent to $$y = \frac{x+5}{2-x}$$. 3. **Domain considerations:** The denominator cannot be zero, so $$2 - x \neq 0 \Rightarrow x \neq 2$$. 4. **Behavior and simplification:** The function is a rational function with a vertical asymptote at $$x=2$$. 5. **No further simplification is possible:** The numerator and denominator share no common factors. 6. **Summary:** The function $$y = \frac{x+5}{2-x}$$ is defined for all real $$x$$ except $$x=2$$, where there is a vertical asymptote. **Final answer:** $$y = \frac{x+5}{2-x}, \quad x \neq 2$$.