\(\dfrac{2}{x-3}+\dfrac{x-5}{x-1}=1.\left(x\ne3;1\right).\\ \Leftrightarrow\dfrac{2x-2+\left(x-5\right)\left(x-3\right)-\left(x-3\right)\left(x-1\right)}{\left(x-3\right)\left(x-1\right)}=0.\\ \Rightarrow2x-2+x^2-3x-5x+15-x^2+4x-3=0.\\ \Leftrightarrow-2x+10=0.\\ \Leftrightarrow x=5.\)