\(\frac{1}{x-2}+\frac{x^2-x-2}{x^2-7x+10}-\frac{2x-4}{x-5}\\ \Leftrightarrow\frac{x-5}{x^2-7x+10}+\frac{x^2-x-2}{x^2-7x+10}-\frac{2x^2-8x+8}{x^2-7x+10}\\ \Leftrightarrow\frac{x-5+x^2-x-2-2x^2+8x-8}{x^2-7x+10}\\ \Leftrightarrow\frac{8x-x^2-15}{x^2-7x+10}\)