x/x+2 - (x-2) ²/2 * (1/x²-4 + 1/x²-4x+4) =

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Алгебра

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16 марта, 19:20

x/x+2 - (x-2) ²/2 * (1/x²-4 + 1/x²-4x+4) =

+1

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Паисий · Answer 1

x / (x+2) - (x-2) ²/2 * (1 / (x²-4) + 1 / (x²-4x+4)) =

= x / (x+2) - (x-2) ²/2 * (1 / (x-2) (x+2) + 1 / (x-2) ²) =

= x / (x+2) - (x-2) ²/2 * ((x-2) / (x-2) ² (x+2) + (x+2) / (x-2) ² (x+2)) =

= x / (x+2) - (x-2) ²/2 * (x-2 + x+2) / (x-2) ² (x+2) =

= x / (x+2) - (x-2) ²/2 * 2x / (x-2) ² (x+2) =

= x / (x+2) - ((x-2) ² * 2x) / 2 (x-2) ² (x+2) =

= x / (x+2) - x / (x+2) = 0