\(\Leftrightarrow\dfrac{x-3}{x-2}+\dfrac{-x-2}{x-4}=\dfrac{16}{5}\\ \Leftrightarrow\dfrac{5\left(x-3\right)\left(x-4\right)+5\left(x-2\right)^2}{5\left(x-2\right)\left(x-4\right)}=\dfrac{16\cdot\left(x-2\right)\left(x-4\right)}{5\left(x-2\right)\left(x-4\right)}\\ \Rightarrow5x^2-20x-15x+60+5x^2+20x+20=16x^2-64x-32x+128\\ \Leftrightarrow10x^2-55x+80=16x^2-96x+128\\ \Leftrightarrow6x^2-41x+48=0\\ \Leftrightarrow\left[{}\begin{matrix}\dfrac{16}{3}\\\dfrac{3}{2}\end{matrix}\right.\)

\(=\dfrac{-2}{6}+\dfrac{15}{6}=\dfrac{13}{6}\)