ĐKXĐ: \(x\notin\left\{2;-2\right\}\)
\(\dfrac{2}{-x^2+6x-8}-\dfrac{x-1}{x-2}=\dfrac{x+3}{x-4}\)
=>\(\dfrac{-2}{\left(x-2\right)\left(x-4\right)}-\dfrac{\left(x-1\right)\left(x-4\right)}{\left(x-2\right)\left(x-4\right)}=\dfrac{\left(x+3\right)\left(x-2\right)}{\left(x-4\right)\left(x-2\right)}\)
=>\(-2-\left(x-1\right)\left(x-4\right)=\left(x+3\right)\left(x-2\right)\)
=>\(-2-\left(x^2-5x+4\right)=x^2+x-6\)
=>\(-2-x^2+5x-4-x^2-x+6=0\)
=>\(-2x^2+4x=0\)
=>-2x(x-2)=0
=>x(x-2)=0
=>\(\left[{}\begin{matrix}x=0\left(nhận\right)\\x=2\left(loại\right)\end{matrix}\right.\)
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