[tex] \frac{x-1}{x+2} \ \textgreater \ \frac{x-2}{x+1} +3 \ \textless \ =\ \textgreater \ \frac{x-1}{x+2} \ \textgreater \ \frac{x-2+3x+3}{x+1} \ \textless \ =\ \textgreater \ \frac{x-1}{x+2} \ \textgreater \ \frac{4x+1}{x+1} [/tex]
inmultim cu (x+2)(x+1)
(x-1)(x+1) > (4x+1)(x+2) <=> [tex] x^{2} -1 \ \textgreater \ 4 x^{2} +8x+x+2 \ \textless \ =\ \textgreater \ -3x^{2} -9x-3 \ \textgreater \ 0 \ \textless \ =\ \textgreater \ 3x^{2} +9x+3[/tex][tex]\ \textless \ 0 \ \textless \ =\ \textgreater \ [/tex]
Δ=45
[tex] \left \{ {{x_{1} =- \frac{3+ \sqrt{5} }{2} } \atop {x_{2} =- \frac{3- \sqrt{5} }{2}} \right. \\ [/tex]
Facem graficul si observam pe care intervale x<0
R-s: x ∈ {[tex]- \frac{3+ \sqrt{5} }{2}; - \frac{3- \sqrt{5} }{2}[/tex]}
