Упростите выражение , help me please
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Ответил m11m
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a)
![frac{(a-b)^{-2}+2(a^2-b^2)^{-1}+(a+b)^{-2}}{(a+b)^2+2(a^2-b^2)+(a-b)^2}= frac{((a-b)^{-1}+(a+b)^{-1})^2}{((a+b)+(a-b))^2} = \ \
= frac{( frac{1}{a-b}+ frac{1}{a+b} )^2}{(2a)^2}= frac{( frac{a+b+a-b}{(a-b)(a+b)} )^2}{(2a)^2} = frac{(2a)^2}{(a^2-b^2)^2*(2a)^2} = \ \
= frac{1}{(a^2-b^2)^2}=(a^2-b^2)^{-2}](https://tex.z-dn.net/?f=+frac%7B%28a-b%29%5E%7B-2%7D%2B2%28a%5E2-b%5E2%29%5E%7B-1%7D%2B%28a%2Bb%29%5E%7B-2%7D%7D%7B%28a%2Bb%29%5E2%2B2%28a%5E2-b%5E2%29%2B%28a-b%29%5E2%7D%3D+frac%7B%28%28a-b%29%5E%7B-1%7D%2B%28a%2Bb%29%5E%7B-1%7D%29%5E2%7D%7B%28%28a%2Bb%29%2B%28a-b%29%29%5E2%7D+%3D+%5C++%5C+%0A%3D+frac%7B%28+frac%7B1%7D%7Ba-b%7D%2B+frac%7B1%7D%7Ba%2Bb%7D++%29%5E2%7D%7B%282a%29%5E2%7D%3D++frac%7B%28+frac%7Ba%2Bb%2Ba-b%7D%7B%28a-b%29%28a%2Bb%29%7D+%29%5E2%7D%7B%282a%29%5E2%7D+%3D+frac%7B%282a%29%5E2%7D%7B%28a%5E2-b%5E2%29%5E2%2A%282a%29%5E2%7D+%3D+%5C++%5C+%0A%3D+frac%7B1%7D%7B%28a%5E2-b%5E2%29%5E2%7D%3D%28a%5E2-b%5E2%29%5E%7B-2%7D+ "frac{(a-b)^{-2}+2(a^2-b^2)^{-1}+(a+b)^{-2}}{(a+b)^2+2(a^2-b^2)+(a-b)^2}= frac{((a-b)^{-1}+(a+b)^{-1})^2}{((a+b)+(a-b))^2} = \ \
= frac{( frac{1}{a-b}+ frac{1}{a+b} )^2}{(2a)^2}= frac{( frac{a+b+a-b}{(a-b)(a+b)} )^2}{(2a)^2} = frac{(2a)^2}{(a^2-b^2)^2*(2a)^2} = \ \
= frac{1}{(a^2-b^2)^2}=(a^2-b^2)^{-2}")
б)
![frac{(x+y)(x-y)^{-1}+(x-y)(x+y)^{-1}-2}{(x+y)(x-y)^{-1}-(x-y)(x+y)^{-1}}= frac{ frac{x+y}{x-y}+ frac{x-y}{x+y}-2 }{ frac{x+y}{x-y}- frac{x-y}{x+y} }= \ \
= frac{ frac{(x+y)^2+(x-y)^2-2(x-y)(x+y)}{(x-y)(x+y)} }{ frac{(x+y)^2-(x-y)^2}{(x-y)(x+y)} }= frac{(x+y-(x-y))^2}{(x+y-(x-y))(x+y+x-y)}= \ \
= frac{(2y)^2}{2y*2x}= frac{2y}{2x}= frac{y}{x}](https://tex.z-dn.net/?f=+frac%7B%28x%2By%29%28x-y%29%5E%7B-1%7D%2B%28x-y%29%28x%2By%29%5E%7B-1%7D-2%7D%7B%28x%2By%29%28x-y%29%5E%7B-1%7D-%28x-y%29%28x%2By%29%5E%7B-1%7D%7D%3D+frac%7B+frac%7Bx%2By%7D%7Bx-y%7D%2B+frac%7Bx-y%7D%7Bx%2By%7D-2++%7D%7B+frac%7Bx%2By%7D%7Bx-y%7D-+frac%7Bx-y%7D%7Bx%2By%7D++%7D%3D+%5C++%5C+%0A%3D+frac%7B+frac%7B%28x%2By%29%5E2%2B%28x-y%29%5E2-2%28x-y%29%28x%2By%29%7D%7B%28x-y%29%28x%2By%29%7D+%7D%7B+frac%7B%28x%2By%29%5E2-%28x-y%29%5E2%7D%7B%28x-y%29%28x%2By%29%7D+%7D%3D+frac%7B%28x%2By-%28x-y%29%29%5E2%7D%7B%28x%2By-%28x-y%29%29%28x%2By%2Bx-y%29%7D%3D+%5C++%5C+%0A%3D+frac%7B%282y%29%5E2%7D%7B2y%2A2x%7D%3D+frac%7B2y%7D%7B2x%7D%3D+frac%7By%7D%7Bx%7D+++++++ "frac{(x+y)(x-y)^{-1}+(x-y)(x+y)^{-1}-2}{(x+y)(x-y)^{-1}-(x-y)(x+y)^{-1}}= frac{ frac{x+y}{x-y}+ frac{x-y}{x+y}-2 }{ frac{x+y}{x-y}- frac{x-y}{x+y} }= \ \
= frac{ frac{(x+y)^2+(x-y)^2-2(x-y)(x+y)}{(x-y)(x+y)} }{ frac{(x+y)^2-(x-y)^2}{(x-y)(x+y)} }= frac{(x+y-(x-y))^2}{(x+y-(x-y))(x+y+x-y)}= \ \
= frac{(2y)^2}{2y*2x}= frac{2y}{2x}= frac{y}{x}")
б)
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