X/x+2-(x-2)²/2* (1/x²-4 +1/x²-4x+4)= - вопрос №193694122214144 от gv8ux 13.12.2021 01:36

Question

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

gv8ux · Answer

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