Question

Exercitiul 1 din poza.

Answer 1

x^2+8x+15=(x+3)(x+5)
x^2+7x+12=(x+3)(x+4)
E(x)=(x+5)/(x+4)

Answer 2

$E(x) = \frac{ {x}^{2} + 8x + 15 }{ {x}^{2} + 7x + 12 } \\ \\ E(x) = \frac{ {x}^{2} + 3x + 5x + 15 }{ {x}^{2} + 3x + 4x + 12 } \\ \\ E(x) = \frac{x( \frac{ {x}^{2} }{x} + \frac{3x}{x}) + 5( \frac{5x}{5} + \frac{3 \times 5}{5}) }{x( \frac{ {x}^{2} }{x} + \frac{3x}{x}) + {2}^{2}( \frac{ {2}^{2} \times x }{ {2}^{2} } + \frac{ {2}^{2} \times 3 }{ {2}^{2} }) } \\ \\ E(x) = \frac{x( {x}^{2 - 1} + 3) + 5(x + 3) }{x( {x}^{2 - 1} + 3) + {2}^{2}(x + 3) } \\ \\ E(x) = \frac{x(x + 3) + 5(x + 3)}{x(x + 3) + {2}^{2}(x + 3) } \\ \\ E(x) = \frac{(x + 3)( \frac{x(x + 3)}{x + 3} + \frac{5(x + 3)}{x + 3}) }{(x + 3)( \frac{x(x + 3)}{x + 3} + \frac{ {2}^{2}(x + 3) }{x + 3}) } \\ \\ E(x) = \frac{(x + 3)(x + 5)}{(x + 3)(x + {2}^{2}) } \\ \\ E(x) = \frac{(x + 3)(x + 5)}{(x + 3)(x + 4)} \\ \\ E(x) = \frac{x + 5}{x + 4}$