rút gọn `E=((x^2 -x+2)/(x^2 -x-2)-x/(x^2 -2x)): (1-x)/(2-x)`

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1. Giải đáp + Lời giải và giải thích chi tiết:

   E = ([x^2 – x + 2]/[x^2 – x – 2] – x/[x^2 – 2x]) : (1 – x)/(2 – x)

   = ([x^2 – x + 2]/[(x^2 + x) – (2x + 2)] – x/[x.(x – 2)]) : (1 – x)/(2 – x)

   = ([x^2 – x + 2]/[x.(x + 1) – 2.(x + 1)] – x/[x.(x – 2)]) : (1 – x)/(2 – x)

   = ([x^2 – x + 2]/[(x + 1).(x – 2)] – x/[x.(x – 2)]) : (1 – x)/(2 – x)

   = [x.(x^2 – x+ 2) – x.(x + 1)]/[x.(x + 1).(x – 2)] : (1 – x)/(2 – x)

   = [x^3 – x^2 + 2x – x^2 – x]/[x.(x + 1).(x – 2)] : (1 – x)/(2 – x)

   = [x^3 – 2x^2 + x]/[x.(x + 1).(x – 2)] : (1 – x)/(2 – x)

     = [x.(x^2 – 2x + 1)]/[x.(x + 1).(x – 2)] : (1 – x)/(2 – x)

   = [x.(x – 1)^2]/[x.(x + 1).(x – 2)] : (1 – x)/(2 – x)

   = [(x – 1)^2]/[(x + 1).(x – 2)] : [-(x – 1)]/[-(x – 2)]

   = [(x – 1)^2]/[(x + 1).(x – 2)] . (x – 2)/(x-  1)

   = [x – 1]/[x + 1]

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