Question

Mentionati conditiile in care fractiile date sunt definite si simplificati-le :

$\frac{4 x^{2}+ 20x + 25 }{4 x^{2}-25 }$
$\frac{ x^{3}+3 x^{2}+3x +1 }{2x( x^{2} +2x+1)}$
$\frac{ 2x^{3}+2x }{ x^{4} -1}$
Multumesc anticipat celor care vor sa ma ajute !

Answer 1

[tex] \frac{4x^2+20x+25}{4x^2-25}= \frac{(2x+5)^2}{(2x+5)(2x-5)}= \frac{2x+5}{2x-5} \\ C.E: \\ 2x+5 \ne 0 \longrightarrow x \ne - \frac{5}{2} \\ 2x-5 \ne 0 \longrightarrow x \ne \frac{5}{2} \\ \boxed{x \in R- \{ \pm \frac{5}{2}\}} \\ \\ \\ \frac{2x^3+2x}{(x^2+1)(x^2-1)}= \frac{2x(x^2+1)}{(x^2-1)(x^2+1)} = \frac{2x}{x^2-1} \\ C.E: \\ x^2-1 \ne 0 \Longrightarrow x \ne 1 \\ \boxed{x \in R-\{1\}} \\ \\ [/tex]