$ \displaystyle \frac{2x-y}{3x+2y}=k \\ 2x-y=3kx+2ky \\ 2x-3kx=y+2ky \\ x(2-3k)=y(1+2k) \\ \displaystyle \frac x y= \frac{1+2k}{2-3k} \Rightarrow k \neq -\frac 1 2 \text{ ve } k \neq \frac{2}{3}\\ \displaystyle \frac{y-x}{y+x}=\frac{y-y( \frac{1+2k}{2-3k})}{y+y(\frac{1+2k}{2-3k})}= \frac{2-3k-1-2k}{2-3k+1+2k}=\frac{1-5k}{3-k} \\ \displaystyle k=- \frac 1 2 \text{ olsaydı ifade }\frac{1+2,5}{3+0,5}=1 \text{ olurdu ki } k\neq -\frac 1 2 \text{ eşitsizliği geçersiz olurdu.}$