[tex]zal.~~x+1\neq 0~~\Rightarrow~~x\neq -1\\D=R -\{ -1 \}\\\\\dfrac{2x-3}{x+1} =x-\frac{5}{3} \\\\\dfrac{2x-3}{x+1} =\dfrac{3x-5}{3} \\\\(x+1)\cdot (3x-5)=3\cdot (2x-3)\\\\3x^{2} -5x+3x-5=6x-9\\\\3x^{2} -2x-6x-5+9=0\\\\3x^{2} -8x+4=0\\a=3,~~b=-8,~~c=4\\\Delta=b^{2} -4ac\\\\\Delta=(-8)^{2} -4\cdot 3\cdot 4=64-48=16,~~\sqrt{\Delta} =4\\\\[/tex]
[tex]x_{1} =\dfrac{-b-\sqrt{\Delta} }{2a} ~~\lor~~x_{2} =\dfrac{-b+\sqrt{\Delta} }{2a} \\\\(~~x_{1} =\dfrac{8-4}{6} =\dfrac{2}{3} ~~\lor~~x_{2} =\dfrac{8+4}{6} =2~~)~~\land~~x \in D~~\Rightarrow ~~x_{1} =\dfrac{2}{3} ~~\lor~~x_{2} =2[/tex]
