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а) ![( frac{2x}{x-1} )^2*( frac{x^2-2x+1}{2x} )^2-x^2= frac{4x^2}{(x-1)^2} *frac{(x-1)^4}{4x^2} -x^2=(x-1)^2-x^2= \ =x^2-2x+1-x^2=-2x+1 ( frac{2x}{x-1} )^2*( frac{x^2-2x+1}{2x} )^2-x^2= frac{4x^2}{(x-1)^2} *frac{(x-1)^4}{4x^2} -x^2=(x-1)^2-x^2= \ =x^2-2x+1-x^2=-2x+1](https://tex.z-dn.net/?f=%28+frac%7B2x%7D%7Bx-1%7D+%29%5E2%2A%28+frac%7Bx%5E2-2x%2B1%7D%7B2x%7D+%29%5E2-x%5E2%3D+frac%7B4x%5E2%7D%7B%28x-1%29%5E2%7D+%2Afrac%7B%28x-1%29%5E4%7D%7B4x%5E2%7D++-x%5E2%3D%28x-1%29%5E2-x%5E2%3D+%5C+%3Dx%5E2-2x%2B1-x%5E2%3D-2x%2B1)
б)![( frac{3}{x-1}+ frac{2x}{x+1} ): frac{4x^2+2x+6}{x^2-1}= frac{3(x+1)+2x(x-1)}{x^2-1}* frac{x^2-1}{4x^2+2x+6} = \ = frac{3x+3+2x^2-2x}{2(2x^2+x+3)}= frac{2x^2+x+3}{2(2x^2+x+3)}= frac{1}{2} ( frac{3}{x-1}+ frac{2x}{x+1} ): frac{4x^2+2x+6}{x^2-1}= frac{3(x+1)+2x(x-1)}{x^2-1}* frac{x^2-1}{4x^2+2x+6} = \ = frac{3x+3+2x^2-2x}{2(2x^2+x+3)}= frac{2x^2+x+3}{2(2x^2+x+3)}= frac{1}{2}](https://tex.z-dn.net/?f=%28+frac%7B3%7D%7Bx-1%7D%2B+frac%7B2x%7D%7Bx%2B1%7D++%29%3A+frac%7B4x%5E2%2B2x%2B6%7D%7Bx%5E2-1%7D%3D+frac%7B3%28x%2B1%29%2B2x%28x-1%29%7D%7Bx%5E2-1%7D%2A+frac%7Bx%5E2-1%7D%7B4x%5E2%2B2x%2B6%7D+%3D+%5C+%3D+frac%7B3x%2B3%2B2x%5E2-2x%7D%7B2%282x%5E2%2Bx%2B3%29%7D%3D+frac%7B2x%5E2%2Bx%2B3%7D%7B2%282x%5E2%2Bx%2B3%29%7D%3D+frac%7B1%7D%7B2%7D+)
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