1. **State the problem:** We are given two functions: $$f(x) = \frac{x-2}{x+2}$$ and $$g(x) = \frac{1}{x'}$$ where $x'$ is the variable in $g(x)$ (apostrophe included as part of the variable). We need to find the sum $f(x) + g(x)$. 2. **Write the sum:** $$f(x) + g(x) = \frac{x-2}{x+2} + \frac{1}{x'}$$ 3. **Find a common denominator:** The common denominator is $(x+2)x'$. 4. **Rewrite each fraction with the common denominator:** $$\frac{x-2}{x+2} = \frac{(x-2) x'}{(x+2) x'}$$ $$\frac{1}{x'} = \frac{x+2}{(x+2) x'}$$ 5. **Add the fractions:** $$\frac{(x-2) x'}{(x+2) x'} + \frac{x+2}{(x+2) x'} = \frac{(x-2) x' + (x+2)}{(x+2) x'}$$ 6. **Simplify the numerator:** $$ (x-2) x' + (x+2) = x x' - 2 x' + x + 2 $$ 7. **Final answer:** $$f(x) + g(x) = \frac{x x' - 2 x' + x + 2}{(x+2) x'}$$