Question

Cu se rezolva acest exercitiu x+1/x-1>x+3/x+2 bara aia ete linie de fractie ca sa stiti

Answer 1

[tex]\frac{x+1}{x-1}\ \textgreater \ \frac{x+3}{x+2} \\ \\ \frac{x+1}{x-1}-\frac{x+3}{x+2}\ \textgreater \ \frac{x+3}{x+2}-\frac{x+3}{x+2} \\ \\ \frac{x+1}{x-1}-\frac{x+3}{x+2}\ \textgreater \ 0 \\ \\ \frac{x+1}{x-1}-\frac{x+3}{x+2} \\ \\ =\frac{\left(x+1\right)\left(x+2\right)}{\left(x+2\right)\left(x-1\right)}-\frac{\left(x+3\right)\left(x-1\right)}{\left(x+2\right)\left(x-1\right)} \\ \\ =\frac{\left(x+1\right)\left(x+2\right)-\left(x+3\right)\left(x-1\right)}{\left(x+2\right)\left(x-1\right)} \\ \\ [/tex][tex]\left(x+1\right)\left(x+2\right)-\left(x+3\right)\left(x-1\right) \\ \\ =x^2+3x+2-\left(x+3\right)\left(x-1\right) \\ \\ =x^2+3x+2-x^2-2x+3 \\ \\ =x^2-x^2+3x-2x+2+3 \\ \\ =x^2-x^2+x+2+3 \\ \\ =x+2+3 \\ \\ =x+5 \\ \\ =\frac{x+5}{\left(x+2\right)\left(x-1\right)} \\ \\ \frac{x+5}{\left(x+2\right)\left(x-1\right)}\ \textgreater \ 0 \\ \\ -5\ \textless \ x\ \textless \ -2\quad \mathrm{sau}\quad \:x\ \textgreater \ 1[/tex]