\(\dfrac{x}{x+3}-\dfrac{x-2}{2x-6}=\dfrac{x+2}{x^2-9}\left(ĐKXĐ:x\ne-3;x\ne3\right)\)
\(\Rightarrow2x\left(x-3\right)-\left(x-2\right)\left(x+3\right)=2\left(x+2\right)\)
\(\Leftrightarrow2x^2-6x-\left(x^2+x-6\right)=2x+4\)
\(\Leftrightarrow2x^2-6x-x^2-x+6-2x-4=0\)
\(\Leftrightarrow x^2-9x+2=0\)
\(\Leftrightarrow x^2-2.x.\dfrac{9}{2}+\dfrac{81}{4}-\dfrac{73}{4}=0\)
\(\Leftrightarrow\left(x-\dfrac{9}{2}\right)^2+\dfrac{73}{4}=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-\dfrac{9}{2}=\dfrac{\sqrt{73}}{2}\\x-\dfrac{9}{2}=\dfrac{-\sqrt{73}}{2}\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{9+\sqrt{73}}{2}\left(n\right)\\x=\dfrac{9-\sqrt{73}}{2}\left(n\right)\end{matrix}\right.\)
đk: x#-3;x#3
\(\dfrac{x}{x+3}-\dfrac{x-2}{2x-6}=\dfrac{x+2}{x^2-9}\)
<=> \(\dfrac{x}{x+3}-\dfrac{x-2}{2\left(x-3\right)}-\dfrac{x+2}{x^2-9}=0\)
<=> \(\dfrac{2x\left(x-3\right)}{2\left(x^2-9\right)}-\dfrac{\left(x-2\right)\left(x+3\right)}{2\left(x^2-9\right)}-\dfrac{2\left(x+2\right)}{2\left(x^2-9\right)}=0\)
<=>\(\dfrac{2x^2-6x-x^2-x+6-2x-4}{2\left(x^2-9\right)}=\dfrac{x^2-9x+2}{2\left(x^2-9\right)}=0\)
<=> x^2-9x+2=0
