\(\dfrac{x-1}{x-2}+\dfrac{x-3}{x-4}=\dfrac{2}{\left(2-x\right)\left(x-4\right)}\)
\(\Leftrightarrow\dfrac{\left(x-1\right)\left(x-4\right)}{\left(x-2\right)\left(x-4\right)}+\dfrac{\left(x-3\right)\left(x-2\right)}{\left(x-2\right)\left(x-4\right)}=\dfrac{-2}{\left(x-2\right)\left(x-4\right)}\) \(\Leftrightarrow x^2-5x+4+x^2-5x+6=-2\)
\(\Leftrightarrow2x^2-10x+12=0\)
\(\Leftrightarrow2x^2-4x-6x+12=0\)
\(\Leftrightarrow\left(2x^2-4x\right)-\left(6x-12\right)=0\)
\(\Leftrightarrow2x\left(x-2\right)-6\left(x-2\right)=0\)
\(\Leftrightarrow\left(x-2\right)\left(2x-6\right)=0\)
suy ra x = 2 hoặc x = 3
\(\)
DK : x≠2,x≠4
pt<=> \(\dfrac{\left(x-1\right)\left(x-4\right)}{\left(x-2\right)\left(x-4\right)}+\dfrac{\left(x+3\right)\left(x-2\right)}{\left(x-2\right)\left(x-4\right)}=\dfrac{-2}{\left(x-2\right)\left(x-4\right)}\)
=> (x-1)(x-4)+(x+3)(x-2)=-2
=> x2-5x+4+x2+x-6+2=0
=> 2x2-4x=0
=> x(x-2)=0
=> x=0(TM) hoac x=2(KTM)
