a) A = \(\frac{1}{x-2}+\frac{x^2-x-2}{x^2-7x+10}-\frac{2x-4}{x-5}\)
= \(\frac{x-5+x^2-x-2-\left(2x-4\right)\left(x-2\right)}{\left(x-5\right)\left(x-2\right)}\)
= \(\frac{x^2-7-2x^2+4x+4x-8}{\left(x-5\right)\left(x-2\right)}\)
= \(\frac{-x^2+8x-15}{\left(x-5\right)\left(x-2\right)}\)
= \(\frac{\left(x-5\right)\left(x-3\right)}{\left(x-5\right)\left(x-2\right)}\)
= \(\frac{x-3}{x-2}\)