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