Question

\(\dfrac{x-3}{x-2}-\dfrac{x-2}{x-4}=3\dfrac{1}{5}\)

Answer 1

\(\Rightarrow\dfrac{x-3}{x-2}-\dfrac{x-2}{x-4}-\dfrac{16}{5}=0\)

\(\Rightarrow\dfrac{5\left(x-4\right)\left(x-3\right)-5\left(x-2\right)\left(x-4\right)-16\left(x-4\right)\left(x-2\right)}{5\left(x-2\right)\left(x-4\right)}=0\)

\(\Rightarrow5\left(x^2-3x-4x+12\right)-5\left(x^2-4x-2x+8\right)-16\left(x^2-2x-4x+8\right)=0\)

\(\Rightarrow5\left(x^2-7x+12\right)-5\left(x^2-6x+8\right)-16\left(x^2-6x+8\right)=0\)

\(\Rightarrow5x^2-35x+60-5x^2+30x-40-16x^2+96x-128=0\)

\(\Rightarrow-16x^2+91x-108=0\)

\(\Rightarrow\left[{}\begin{matrix}x_1=4\\x_2=\dfrac{27}{16}\end{matrix}\right.\)