[tex]a) \left \{ {{\frac{2}{x-y}+\frac{3}{x+y}=-1} \atop {\frac{3}{x-y}-\frac{2}{x+y}=5}} \right. \\
Notam:\frac{1}{x-y}=a, \frac{1}{x+y}=b\\
\left \{ {{2a+3b=-1}|\cdot 3 \atop {3a-2b=5}|\cdot 2} \right. \Leftrightarrow \left \{ {{6a+9b=-3} \atop {6a-4b=10}} \right. \\
Le\ scadem: \ \ \ \ \ 13b=-13\Rightarrow b=-1\\
2a-3=-1\Rightarrow a=1\\
Asadar:\\
\left \{ {{\frac{1}{x-y}=1} \atop {\frac{1}{x+y}=-1}} \right. \Leftrightarrow \left \{ {{x-y=1} \atop {-x-y=1}} \right.\\
[/tex]
[tex]Le\ adunam: -2y=2\Rightarrow \boxed{y=-1}\\
x-y=1\\
x+1=1\\
\boxed{x=0}\\
\\
b) \left \{ {{3[x]+2[y]=-1} \atop {[x]-3[y]=-4}|\cdot3} \right.\Leftrightarrow \left \{ {{3[x]+2[y]=-1} \atop {3[x]-9[y]=-12}} \right.\\
Le\ scadem:\ \ \ \ \ \ \ \ \ \ 11[y]=11\\
.\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [y]=1\Rightarrow y\in[1,2)\\
3[x]+2=-1\\
3[x]=-3\\
{[x]=-1\Rightarrow x\in [-1, -2)}
[/tex]
