a) \(\dfrac{x-2}{x-4}-\dfrac{1}{x-2}=-2\)
\(\Leftrightarrow\dfrac{\left(x-2\right)\left(x-2\right)-1\left(x-4\right)}{\left(x-4\right)\left(x-2\right)}=\dfrac{-2\left(x-4\right)\left(x-2\right)}{\left(x-4\right)\left(x-2\right)}\)\(\Leftrightarrow x^2-4x+4-x+4=-2x^2+4x+8x-16\)
\(\Leftrightarrow x^2-5x-4x-8x+2x^2=-16-4-4\)
\(\Leftrightarrow3x^2-17x=-24\)
\(\Leftrightarrow3x^2-17x+24=0\)
\(\Leftrightarrow\left(x-3\right)\left(3x-8\right)\)
=> x -3 = 0 hoặc 3x - 8 = 0
=> x = 3 hoặc x = 8/3
\(\dfrac{5x-1}{4}+\dfrac{x+2}{6}=\dfrac{x}{8}\)
\(\Leftrightarrow\dfrac{\left(5x-1\right).6+\left(x+2\right).4}{24}=\dfrac{3x}{24}\)
\(\Leftrightarrow30x-6+4x+8=3x\)
\(\Leftrightarrow30x+4x-3x=6-8\)
\(\Leftrightarrow30x+4x-6+8-3x=0\)
\(\Leftrightarrow31x-2=0\)
\(\Leftrightarrow x=\dfrac{2}{31}\)
