đk x khác 2 ;3
\(\dfrac{x+3}{x-2}+\dfrac{x+2}{x-3}=2\)
\(\Rightarrow\left(x+3\right)\left(x-3\right)+\left(x+2\right)\left(x-2\right)=2\left(x-2\right)\left(x-3\right)\)
\(\Leftrightarrow x^2-9+x^2-4=2\left(x^2-5x+6\right)\)
\(\Leftrightarrow2x^2-13=2x^2-10x+12\Leftrightarrow10x-25=0\Leftrightarrow x=\dfrac{5}{2}\left(tm\right)\)
\(\dfrac{x+3}{x-2}+\dfrac{x+2}{x-3}=2\left(x\ne2;x\ne3\right)\\ \Leftrightarrow\dfrac{\left(x-3\right)\left(x+3\right)}{\left(x-2\right)\left(x-3\right)}+\dfrac{\left(x+2\right)\left(x-2\right)}{\left(x-2\right)\left(x-3\right)}=\dfrac{2\left(x-3\right)\left(x-2\right)}{\left(x-2\right)\left(x-3\right)}\\ \Leftrightarrow\left(x^2-9\right)+\left(x^2-4\right)=2\left(x^2-2x-3x+6\right)\\ \Leftrightarrow2x^2-13=2x^2-10x+12\\ \Leftrightarrow-10x+12=-13\\ \Leftrightarrow-10x=-25\\ \Leftrightarrow x=\dfrac{25}{10}\\ \Leftrightarrow x=\dfrac{5}{2}\left(tm\right)\)