Question

Rezolvă în R ecuația:
Urgent, vă rog mult.. marchez cel mai bun

Answer 1

Conditia ecuatiei este x-1≠0 <=> x≠1
3(x²+x-2)=(x-1)(2x+3)
3x²+3x-6=2x²+x-3
x²+2x-3=0
Δ=4+12
Δ=16 =>√Δ=4
x₁=(-2-4)/2=-3
x₂=(-2+4)/2=1, care nu poate fi solutie
=>sol.{-3}

Answer 2

   
Avem de rezolvat o ecuatie de gradul 2 reductibila la gradul 1.

[tex]\displaystyle\\ \frac{x^2+x-2}{x-1}=\frac{2x+3}{3}\\\\ Conditii:~~~x-1 \neq 0~~\Rightarrow~~x\neq 1~~\Rightarrow~~x\in \mathbb{R}-\{1\}\\\\ \text{Rezolvare:}\\\\ \frac{x^2+x-2}{x-1}=\frac{2x+3}{3}~~~~unde~~~x=2x-x\\\\ \frac{x^2+2x-x-2}{x-1}=\frac{2x+3}{3}\\\\ \frac{x(x + 2)-(x+2)}{x-1}=\frac{2x+3}{3}\\\\ \frac{(x + 2)(x-1)}{x-1}=\frac{2x+3}{3}~~~\text{Simplificam prima fractie cu } ~~(x-1)\\\\ x+2=\frac{2x+3}{3}\\\\ 3(x+2)=2x+3\\ 3x+6=2x+3\\ 3x-2x=3-6\\ x = \boxed{-3} [/tex]