1. **State the problem:** Simplify the expression $$\frac{x}{x+2} - \frac{7}{x-2}$$ and identify which option (a, b, c, d, or e) matches the simplified form. 2. **Formula and rules:** To subtract two fractions, find a common denominator and combine the numerators: $$\frac{a}{b} - \frac{c}{d} = \frac{ad - bc}{bd}$$ 3. **Find the common denominator:** The denominators are $x+2$ and $x-2$, so the common denominator is: $$ (x+2)(x-2) = x^2 - 4 $$ 4. **Rewrite each fraction with the common denominator:** $$ \frac{x}{x+2} = \frac{x(x-2)}{(x+2)(x-2)} = \frac{x^2 - 2x}{x^2 - 4} $$ $$ \frac{7}{x-2} = \frac{7(x+2)}{(x-2)(x+2)} = \frac{7x + 14}{x^2 - 4} $$ 5. **Subtract the numerators:** $$ \frac{x^2 - 2x}{x^2 - 4} - \frac{7x + 14}{x^2 - 4} = \frac{(x^2 - 2x) - (7x + 14)}{x^2 - 4} $$ 6. **Simplify the numerator:** $$ x^2 - 2x - 7x - 14 = x^2 - 9x - 14 $$ 7. **Final simplified expression:** $$ \frac{x^2 - 9x - 14}{x^2 - 4} $$ 8. **Match with options:** This matches option (c). **Answer:** (c) $$\frac{x^2 - 9x - 14}{x^2 - 4}$$