Question

\(\dfrac{x-3}{x-2}\)+\(\dfrac{x-2}{x-4}\)=-1

Answer 1

\(\dfrac{x-3}{x-2}+\dfrac{x-2}{x-4}=-1\left(x\ne2;x\ne4\right).\\ \Leftrightarrow\dfrac{\left(x-3\right)\left(x-4\right)+\left(x-2\right)^2+\left(x-2\right)\left(x-4\right)}{\left(x-2\right)\left(x-4\right)}=0.\\ \Rightarrow x^2-4x-3x+12+x^2-4x+4+x^2-4x-2x+8=0.\\ \Leftrightarrow3x^2-17x+24=0.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=3\\x=\dfrac{8}{3}\end{matrix}\right.\) (TM).