1)\(-\dfrac{4x-3}{x-5}=\dfrac{29}{3}\Leftrightarrow\dfrac{3-4x}{x-5}=\dfrac{29}{3}\)
\(\Leftrightarrow3\left(3-4x\right)=29\left(x-5\right)\Leftrightarrow9-12x=29x-145\)
\(\Leftrightarrow29x+12x=9+145\Leftrightarrow41x=154\Leftrightarrow x=\dfrac{154}{41}\)
2)\(\dfrac{2x-1}{5-3x}=2\Leftrightarrow2\left(2x-1\right)=5-3x\)
\(\Leftrightarrow4x-2=5-3x\)
\(\Leftrightarrow4x+3x=5+2\Leftrightarrow7x=7\Leftrightarrow x=1\)
3)\(\dfrac{4x-5}{x-1}=2+\dfrac{x}{x-1}\)
\(\Leftrightarrow\dfrac{4x-5}{x-1}=\dfrac{2\left(x-1\right)}{x-1}+\dfrac{x}{x-1}\)
\(\Rightarrow4x-5=2x-2+x\)
\(\Leftrightarrow4x-2x-x=-2+5\)
\(\Leftrightarrow x=3\)
\(1)-\dfrac{4x-3}{x-5}=\dfrac{29}{3} (x \neq 5) \\\Leftrightarrow\dfrac{3-4x}{x-5}=\dfrac{29}{3}\) \(\Leftrightarrow3\left(3-4x\right)=29\left(x-5\right)\\\Leftrightarrow9-12x=29x-145\) \(\Leftrightarrow29x+12x=9+145\\\Leftrightarrow41x=154\\\Leftrightarrow x=\dfrac{154}{41}(TM)\)
Vậy \(S=\left\{\dfrac{154}{41}\right\}\)
\(2)\dfrac{2x-1}{5-3x}=2 (x \neq \dfrac{5}{3}) \)
\(\Leftrightarrow2x-1=2\left(5-3x\right)\\ \Leftrightarrow2x-1=10-6x\\ \Leftrightarrow2x+6x=10+1\\ \Leftrightarrow8x=11\\ \Leftrightarrow x=\dfrac{11}{8}\left(TM\right)\)
Vậy \(S=\left\{\dfrac{11}{8}\right\}\)
\(3)\dfrac{4x-5}{x-1}=2+\dfrac{x}{x-1} (x \neq 1) \\\Leftrightarrow\dfrac{4x-5}{x-1}=\dfrac{2\left(x-1\right)}{x-1}+\dfrac{x}{x-1}\) \(\Leftrightarrow4x-5=2x-2+x\) \(\Leftrightarrow4x-2x-x=-2+5\) \(\Leftrightarrow x=3(TM)\)
Vậy \(S=\left\{3\right\}\)
