Question

[tex] \frac{x^{2} -9}{ x^{2} -4x+3} + \frac{x+2}{x+1} - \frac{ x^{2} +5x+2}{ x^{2} -1}
[/tex] =1 pt orice x apartine r fara -1;1;3 trebuie sa demonstrez asta

Answer 1

Salut,

Ai scris enunțul cu LaTex, bravo, te felicit !

$E(x)=\dfrac{x^2-9}{x^2-4x+3}+\dfrac{x+2}{x+1}-\dfrac{x^2+5x+2}{x^2-1}=\\\\=\dfrac{(x-3)(x+3)}{x^2-3x-x+3}+\dfrac{x+2}{x+1}-\dfrac{x^2+5x+2}{x^2-1}=\\\\=\dfrac{(x-3)(x+3)}{x(x-3)-(x-3)}+\dfrac{x+2}{x+1}-\dfrac{x^2+5x+2}{x^2-1}=\\\\=\dfrac{(x-3)(x+3)}{(x-3)(x-1)}+\dfrac{x+2}{x+1}-\dfrac{x^2+5x+2}{x^2-1}=\\\\=\dfrac{x+3}{x-1}+\dfrac{x+2}{x+1}-\dfrac{x^2+5x+2}{x^2-1}=\\\\=\dfrac{(x+3)(x+1)+(x+2)(x-1)-x^2-5x-2}{x^2-1}=\\\\=\dfrac{x^2+x+3x+3+x^2-x+2x-2-x^2-5x-2}{x^2-1}=\\\\=\dfrac{x^2-1}{x^2-1}=1.$

Green eyes.