1. **State the problem:** Solve the equation $$\frac{x+5}{2-x} = 6$$. 2. **Formula and rules:** To solve a rational equation like this, multiply both sides by the denominator to eliminate the fraction, but be careful about values that make the denominator zero (here, $x \neq 2$). 3. **Multiply both sides by the denominator:** $$\frac{x+5}{2-x} = 6 \implies (x+5) = 6(2-x)$$ 4. **Distribute the right side:** $$x + 5 = 12 - 6x$$ 5. **Bring all terms involving $x$ to one side:** $$x + 6x = 12 - 5$$ $$7x = 7$$ 6. **Divide both sides by 7:** $$\cancel{7}x = \frac{7}{\cancel{7}}$$ $$x = 1$$ 7. **Check for restrictions:** The denominator $2 - x$ cannot be zero, so $x \neq 2$. Since $x=1$ is allowed, it is the solution. **Final answer:** $$x = 1$$