Answer:
A
[tex] \frac{x {}^{2} + 3x + 2}{x {}^{2} + 4x + 3 } \\ = \frac{(x + 2)(x + 1)}{(x + 3)(x + 1)} \\ = \frac{x + 2}{x + 3} [/tex]
E
[tex] \frac{3x {}^{2} + 15x }{x {}^{2} + 10x + 25} \\ = \frac{3x(x + 5)}{(x + 5)(x + 5)} \\ = \frac{3x}{x + 5} [/tex]
H
[tex] \frac{9x - 18}{x {}^{2} - 4} \\ = \frac{9(x - 2)}{(x + 2)(x - 2)} \\ = \frac{9}{x + 2} [/tex]
I
[tex] \frac{x {}^{2} - 36 }{x {}^{2} + 4x - 12} \\ = \frac{(x + 6)(x - 6)}{(x + 6)(x - 2)} \\ = \frac{x - 6}{x - 2} [/tex]
N
[tex] \frac{9x - 36}{x {}^{2} - 8x + 16} \\ = \frac{9(x - 4)}{(x - 4)(x - 4)} \\ = \frac{9}{x - 4} [/tex]
P
[tex] \frac{x {}^{2} - 9}{x {}^{2} - 6x + 9 } \\ = \frac{(x + 3)(x - 3)}{(x - 3)(x - 3)} \\ = \frac{ {x + 3}}{x - 3} [/tex]
Z
[tex] \frac{5x {}^{2} + 10x}{x {}^{2} - 4 } \\ = \frac{5x(x + 2)}{(x + 2)(x - 2)} \\ = \frac{5x}{x - 2} [/tex]
1.
[tex] \frac{x {}^{3} + 12x {}^{2} + 35x }{x {}^{3} + 4x {}^{2} - 21x} \\ = \frac{x(x {}^{2} + 12x + 35)}{x(x {}^{2} +4x - 21)} \\ = \frac{(x + 7)(x + 5)}{(x + 7)(x - 3)} \\ = \frac{x + 5}{x - 3} [/tex]
2.
[tex] \frac{18x {}^{3} + 81x {}^{2} + 63x }{63x {}^{3} + 9x {}^{2} - 54x} \\ = \frac{9x(2x {}^{2} + 9x +7)}{9x(7x {}^{2} + x - 6) } \\ = \frac{(2x + 7)(x + 1)}{(7x - 6)(x + 1)} \\ = \frac{2x + 7}{7x - 6} [/tex]
3.
[tex] \frac{3n {}^{3} - 3n {}^{2} - 3n + 3}{2n {}^{2} - 9n + 7 } \\ = \frac{3(n {}^{3} - n {}^{2} - n + 3) }{(2n - 7)(n - 1)} \\ = \frac{3(n - 1) (n - 1) (n + 1)}{(2n - 7)(n - 1)} \\ = \frac{3(n - 1)(n + 1)}{2n - 7} [/tex]
