Question

Fie expresia E(X) = x²-x-2 supra x²-4 totul de adunat cu x+1 supra x+2.
Determinați valorile reale ale lui X, pentru care
E(X) = 1.
Explicati va rog ce trebuie de facut

Answer 1

   
[tex]\displaystyle\\ E(x)=\frac{x^2-x-2}{x^2-4}+\frac{x+1}{x+2}\\\\ \text{Aducem expresia la o forma mai simpla.}\\ \text{Descompunem in factori numaratorul si numitorul primei fractii.}\\ x^2-x-2=x^2-x-x+x-2=\\ =x^2-2x+x-2=x(x-2)+(x-2)=\boxed{\bf(x-2)(x+1)}\\\\ x^2-4 = \boxed{\bf(x+2)(x-2)}\\\\ E(x) =\frac{x^2-x-2}{x^2-4}+\frac{x+1}{x+2}=\\\\ =\frac{(x-2)(x+1)}{(x+2)(x-2)}+\frac{x+1}{x+2}=~~~\text{Simplificam prima fractie cu (x - 2).}\\\\ =\frac{x+1}{x+2} + \frac{x+1}{x+2}=\boxed{\frac{2x+2}{x+2}} [/tex]


[tex]\displaystyle\\ E(x)=\frac{2x+2}{x+2}\\\\ \text{Rezolvam ecuatia: }\\ E(x) = 1\\\\ \frac{2x+2}{x+2}=1\\\\ 2x+2=x+2\\ 2x-x = 2-2\\ \boxed{\bf x = 0}[/tex]

Answer 2

ai rezolvarea în imagine