1. **State the problem:** Simplify the expression $$\frac{2}{x+2} - \frac{7}{x-2}$$ and compare it with the given options. 2. **Find a common denominator:** The denominators are $x+2$ and $x-2$. The common denominator is $$(x+2)(x-2) = x^2 - 4$$. 3. **Rewrite each fraction with the common denominator:** $$\frac{2}{x+2} = \frac{2(x-2)}{(x+2)(x-2)} = \frac{2x - 4}{x^2 - 4}$$ $$\frac{7}{x-2} = \frac{7(x+2)}{(x-2)(x+2)} = \frac{7x + 14}{x^2 - 4}$$ 4. **Subtract the fractions:** $$\frac{2x - 4}{x^2 - 4} - \frac{7x + 14}{x^2 - 4} = \frac{2x - 4 - (7x + 14)}{x^2 - 4} = \frac{2x - 4 - 7x - 14}{x^2 - 4} = \frac{-5x - 18}{x^2 - 4}$$ 5. **Simplify numerator if possible:** The numerator is $-5x - 18$, which cannot be factored nicely to match any options. 6. **Check options:** - a. $\frac{x-7}{x+2}$ - b. $\frac{x+7}{x+2}$ - c. $\frac{x^2 - 9x - 14}{x^2 - 4}$ - d. $\frac{x^2 - 9x + 14}{x^2 - 4}$ - e. $\frac{x - 7}{4}$ 7. **Factor options c and d numerators:** $$x^2 - 9x - 14 = (x - 7)(x - 2)$$ $$x^2 - 9x + 14 = (x - 7)(x - 2)$$ Actually, $x^2 - 9x + 14 = (x - 7)(x - 2)$ is incorrect; let's factor carefully: $$x^2 - 9x + 14 = (x - 7)(x - 2)$$ $$x^2 - 9x - 14 = (x - 14)(x + 1)$$ (not matching) So option d numerator factors as $(x - 7)(x - 2)$. 8. **Rewrite option d:** $$\frac{(x - 7)(x - 2)}{x^2 - 4} = \frac{(x - 7)(x - 2)}{(x - 2)(x + 2)} = \frac{x - 7}{x + 2}$$ after canceling $x - 2$. 9. **Compare with our simplified expression:** Our simplified expression is $$\frac{-5x - 18}{x^2 - 4}$$ which does not match option d or others. 10. **Conclusion:** None of the options exactly match the simplified expression. However, option a is $$\frac{x - 7}{x + 2}$$ which matches the simplified form of option d after canceling. **Final answer:** The simplified form of the original expression is $$\frac{-5x - 18}{x^2 - 4}$$ which does not match any given options exactly.