Question

ajutati ma va rog help me rezolvare completă

Answer 1

²E(x)=($\frac{x+1}{(x-2)(x-1)}$-$\frac{x-3}{(x-1)(x+3)}$):$\frac{3x-1}{(x+3)(x-2)}$
E(x)=$\frac{(x+1)(x+3)-(x-2)(x-3)}{(x-2)(x-1)(x+3)}$·$\frac{(x+3)(x-2)}{(3x-1)}$
E(x)=$\frac{ x^{2}+3x+x+3- x^{2} +2x+3x-6 }{(x-1)(x-2)(x+3)}$·$\frac{(x+3)(x-2)}{(3x-1)}$
E(x)=$\frac{9x-3}{x-1}$·$\frac{1}{(3x-1)}$
E(x)=$\frac{3(3x-1)}{x-1}$·$\frac{1}{(3x-1)}$
E(x)=$\frac{3}{x-1}$
unde am aplicat metoda disocierii de descompunere in factori
x²-3x+2=x²-1x-2x+2=x(x-1)-2(x-1)=(x-1)(x-2) am cautat doua nr care inmultite sa dea 2 si adunate sa dea 3 ⇒ 1 si 2 ⇒-1x si -2x vom scrie in loc de -3x
x²+2x-3=x²-1x+3x-3=x(x-1)+3(x-1)=(x-1)(x+3) am cautat doua nr care inmultite sa dea 3 si scazute sa dea 2⇒ 1 si 3 ⇒-1x si 3x vom scrie in loc de 2x
x²+x-6=x²+3x-2x-6=x(x+3)-2(x+3)=(x+3)(x-2) am cautat doua nr care inmultite sa dea 6 si scazute sa dea 1⇒ 3 si 2⇒3x si -2x vom scrie in loc de x