Solutions

1.) \frac{x^{2}+12x+35}{x+5}=\frac{(x+5)(x+7)}{x+5}=x+7

2.) \frac{x^{2}+6x-16}{x-2}=\frac{(x-2)(x+8)}{x-2}=x+8

3.) \frac{x^{2}+7x+6}{x^{2}+2x-24}=\frac{(x+1)(x+6)}{(x-4)(x+6)}=\frac{x+1}{x-4}

4.) \frac{x^{2}-6x+9}{x^{2}-9}=\frac{(x-3)(x-3)}{(x+3)(x-3)}=\frac{x-3}{x+3}

5.) \frac{81-x^{2}}{x^{2}-8x-9}=\frac{-(x-9)(x+9)}{(x-9)(x+1)}=\frac{9-x}{x+1}

6.) \frac{2x^{2}-7x-4}{x^{2}-x-12}=\frac{(2x+1)(x-4)}{(x+3)(x-4)}=\frac{2x+1}{x+3}

7.) \frac{3x^{2}+12x-36}{x^{2}-2x}=\frac{3(x^{2}+4x-12)}{x^{2}-2x}=\frac{3(x+6)(x-2)}{x(x-2)}=\frac{3(x+6)}{x}