Răspuns:
[tex] {x}^{2} + 9x + 18 = (x + 6)(x + 3)[/tex]
(x+6)(x+3)=0 => x+6=0=> x= -6
x+3=0=> x= -3
D=R\{ -6; -3}
[tex] {x}^{2} + 8x + 15 = (x + 5)(x + 3)[/tex]
(x+5)(x+3)=0=> x+5=0 => x= -5
x+3=0 => x= -3
D= R\{ -5; -3}
[tex] \frac{ {x}^{2} + 11x + 30 }{ {x}^{2} + 9x + 18 } = \frac{ {x}^{2} + 6x + 5x + 30}{ {x}^{2} + 6x + 3x + 18} = \frac{x(x + 6) + 5(x + 6)}{x(x + 6) + 3(x + 6)} = \frac{(x + 6)(x + 5)}{(x + 6)(x + 3)} = \frac{x + 5}{x + 3} [/tex]
[tex] \frac{ {x}^{2} + 10x + 25 }{ {x}^{2} + 8 x + 15} = \frac{ {(x + 5)}^{2} }{ {x}^{2} + 5x + 3x + 15} = \frac{ {(x + 5)}^{2} }{x(x + 5) + 3(x + 5)} = \frac{ {(x + 5)}^{2} }{(x + 5)(x + 3)} = \frac{x + 5}{x + 3} [/tex]
[tex] \frac{x + 5}{x + 3} = \frac{x + 5}{x + 3} rezulta \: ca \: e1 = e2[/tex]
Explicație pas cu pas:
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