Question: 1. \frac{x^2+5x+6}{x^2-4} = N
2. \frac{x^2-16}{x^2+8x+16} = N
3. \frac{4x+20}{8x+40} = N
4. \frac{x^2+12x+36}{x^2-36} = N
5. \frac{x^2-9}{x^2+4x+3} = N
6. \frac{6x+12}{x^2-4} = N
7. \frac{5x+15}{2x+6} = N
Multiplying and Dividing of RAE
8. \frac{x^2-36}{x^2+12x+36} x \frac{x+6}{x-6} = N
9. \frac{x^2-9}{x^2+4x+3} x \frac{x+1}{x-3} = N
10. \frac{5x}{x^2-16} x \frac{x+4}{10} = N
11. \frac{6x+12}{x^2-4} x \frac{x-2}{3} = N
12. \frac{x^2-6x+9}{1} \frac{x-3}{x+5} = N
13. \frac{4x-8}{x^2-9} \frac{x-2}{x+3} = N
Addition and Subtraction of RAE
14. \frac{5}{x+4} + \frac{3x-2}{x+4} = N
15. \frac{7x-6}{x-5} + \frac{x+4}{x-5} = N
16. \frac{4x+3}{x+2} + \frac{-x+9}{x+2} = N
17. \frac{x}{x^2-36} - \frac{2x+6}{x+6} = N
18. \frac{x}{3x+6} - \frac{12}{x+2} = N
19. \frac{6}{x+1} + \frac{4}{x+5} = N
20. \frac{5}{x+4} - \frac{x-2}{x^2-16} = N
21. \frac{2}{x-3} + \frac{5}{x+6} = N
1. **Problem:** Simplify the rational expression $$\frac{x^2+5x+6}{x^2-4} = N$$
2. **Formula and rules:** Factor numerator and denominator.
3. Factor numerator: $$x^2+5x+6 = (x+2)(x+3)$$
4. Factor denominator: $$x^2-4 = (x-2)(x+2)$$
5. Substitute factors: $$\frac{(x+2)(x+3)}{(x-2)(x+2)}$$
6. Cancel common factor $$\cancel{(x+2)}$$:
$$\frac{\cancel{(x+2)}(x+3)}{(x-2)\cancel{(x+2)}} = \frac{x+3}{x-2}$$
7. **Answer:** $$N = \frac{x+3}{x-2}$$
This completes the simplification of the first rational expression.
Note: The domain excludes values that make the denominator zero, so $$x \neq 2, -2$$.
**q_count:** 21