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8-n³=2³-n³=(2-n)(4+2n+n²)
![1) frac{8-n^3}{2+n}:(2+ frac{n^2}{2+n})= frac{8-n^3}{2+n}:( frac{2(2+n)+n^2}{2+n})= frac{8-n^3}{2+n}:( frac{4+2n+n^2}{2+n})= \ \ = frac{8-n^3}{2+n}cdot ( frac{2+n}{4+2n+n^2})= frac{(2-n)(4+2n+n^2)}{2+n}cdot ( frac{2+n}{4+2n+n^2})= 2-n 1) frac{8-n^3}{2+n}:(2+ frac{n^2}{2+n})= frac{8-n^3}{2+n}:( frac{2(2+n)+n^2}{2+n})= frac{8-n^3}{2+n}:( frac{4+2n+n^2}{2+n})= \ \ = frac{8-n^3}{2+n}cdot ( frac{2+n}{4+2n+n^2})= frac{(2-n)(4+2n+n^2)}{2+n}cdot ( frac{2+n}{4+2n+n^2})= 2-n](https://tex.z-dn.net/?f=1%29+frac%7B8-n%5E3%7D%7B2%2Bn%7D%3A%282%2B+frac%7Bn%5E2%7D%7B2%2Bn%7D%29%3D+frac%7B8-n%5E3%7D%7B2%2Bn%7D%3A%28+frac%7B2%282%2Bn%29%2Bn%5E2%7D%7B2%2Bn%7D%29%3D++frac%7B8-n%5E3%7D%7B2%2Bn%7D%3A%28+frac%7B4%2B2n%2Bn%5E2%7D%7B2%2Bn%7D%29%3D+%5C++%5C+%3D++++frac%7B8-n%5E3%7D%7B2%2Bn%7Dcdot+%28+frac%7B2%2Bn%7D%7B4%2B2n%2Bn%5E2%7D%29%3D++frac%7B%282-n%29%284%2B2n%2Bn%5E2%29%7D%7B2%2Bn%7Dcdot+%28+frac%7B2%2Bn%7D%7B4%2B2n%2Bn%5E2%7D%29%3D+2-n+++++++++++)
![2) frac{n^2}{n-2}cdot frac{7-n^2}{n^2+2n}= frac{n^2}{n-2}cdot frac{7-n^2}{n(n+2)}= frac{n}{n-2}cdot frac{7-n^2}{n+2}=frac{(7-n^2)n}{n^2-4}\ \3)(2-n)-frac{(7-n^2)n}{n^2-4}= frac{(2-n)(n^2-4)-(7-n^2)n}{n^2-4} = frac{2n^2-n^3-8+4n-7n+n^3}{n^2-4} = \ \ = frac{2n^2-3n-8}{n^2-4} 2) frac{n^2}{n-2}cdot frac{7-n^2}{n^2+2n}= frac{n^2}{n-2}cdot frac{7-n^2}{n(n+2)}= frac{n}{n-2}cdot frac{7-n^2}{n+2}=frac{(7-n^2)n}{n^2-4}\ \3)(2-n)-frac{(7-n^2)n}{n^2-4}= frac{(2-n)(n^2-4)-(7-n^2)n}{n^2-4} = frac{2n^2-n^3-8+4n-7n+n^3}{n^2-4} = \ \ = frac{2n^2-3n-8}{n^2-4}](https://tex.z-dn.net/?f=2%29+frac%7Bn%5E2%7D%7Bn-2%7Dcdot+frac%7B7-n%5E2%7D%7Bn%5E2%2B2n%7D%3D++frac%7Bn%5E2%7D%7Bn-2%7Dcdot+frac%7B7-n%5E2%7D%7Bn%28n%2B2%29%7D%3D++frac%7Bn%7D%7Bn-2%7Dcdot+frac%7B7-n%5E2%7D%7Bn%2B2%7D%3Dfrac%7B%287-n%5E2%29n%7D%7Bn%5E2-4%7D%5C+%5C3%29%282-n%29-frac%7B%287-n%5E2%29n%7D%7Bn%5E2-4%7D%3D+frac%7B%282-n%29%28n%5E2-4%29-%287-n%5E2%29n%7D%7Bn%5E2-4%7D+%3D+frac%7B2n%5E2-n%5E3-8%2B4n-7n%2Bn%5E3%7D%7Bn%5E2-4%7D+%3D+%5C+%5C+%3D+frac%7B2n%5E2-3n-8%7D%7Bn%5E2-4%7D)
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спасибо)
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