\(\frac{2}{x-3}+\frac{x-5}{x-1}=1\)
\(\Leftrightarrow\frac{2\left(x-1\right)}{\left(x-3\right)\left(x-1\right)}+\frac{\left(x-3\right)\left(x-5\right)}{\left(x-1\right)\left(x-3\right)}=1\)
\(\Leftrightarrow\frac{2x-2+x^2-8x+15}{\left(x-3\right)\left(x-1\right)}=1\)
\(\Leftrightarrow\frac{x^2-6x+13}{x^2-4x+3}=1\)
\(\Leftrightarrow x^2-6x+13=x^2-4x+3\)
\(\Leftrightarrow2x=10\)
\(\Leftrightarrow x=5\)
Ta có :
\(\frac{2}{x-3}+\frac{x-5}{x-1}=1\)
\(\Leftrightarrow\frac{2\left(x-1\right)}{\left(x-1\right)\left(x-3\right)}+\frac{\left(x-5\right)\left(x-3\right)}{\left(x-1\right)\left(x-3\right)}=\frac{\left(x-1\right)\left(x-3\right)}{\left(x-1\right)\left(x-3\right)}\)
\(\Leftrightarrow\frac{2x-2}{\left(x-1\right)\left(x-3\right)}+\frac{x^2-8x+15}{\left(x-1\right)\left(x-3\right)}=\frac{x^2-4x+3}{\left(x-1\right)\left(x-3\right)}\)
\(\Rightarrow2x-2+x^2-8x+15=x^2-4x+3\)
\(\Leftrightarrow x^2-x^2+2x+4x-8x=3+2-15\)
\(\Leftrightarrow-2x=-10\Leftrightarrow x=5\)
Vậy x = 5 là ngiệm của PT.