Предмет: Алгебра,
автор: bombarek777
помогите плиз алгебра 7 класс
Приложения:
![](https://files.topotvet.com/i/fe5/fe572c8cbfe854ecd703d959a22e28a6.jpg)
bombarek777:
там n
Ответы
Автор ответа:
1
б)
![\frac{a^{3n-1}b^{n+1}-4a^{n-1}b^{n+1}}{4a^nb^{n-1}-4a^{2n}b^{n-1}+a^{3n}b^{n-1}}=\frac{b^{n+1}(a^{3n-1}-4a^{n-1})}{b^{n-1}(4a^n-4a^{2n}+a^{3n})}=\\=\frac{b^{n+1-(n-1)}*a^{n-1}(a^{2n}-4)}{a^n(4-4a^n+a^{2n})}=\frac{b^2*a^{n-1-n}(a^n-2)(a^n+2)}{(a^n-2)^2}=\\=\frac{b^2*(a^n+2)}{a*(a^n-2)} \frac{a^{3n-1}b^{n+1}-4a^{n-1}b^{n+1}}{4a^nb^{n-1}-4a^{2n}b^{n-1}+a^{3n}b^{n-1}}=\frac{b^{n+1}(a^{3n-1}-4a^{n-1})}{b^{n-1}(4a^n-4a^{2n}+a^{3n})}=\\=\frac{b^{n+1-(n-1)}*a^{n-1}(a^{2n}-4)}{a^n(4-4a^n+a^{2n})}=\frac{b^2*a^{n-1-n}(a^n-2)(a^n+2)}{(a^n-2)^2}=\\=\frac{b^2*(a^n+2)}{a*(a^n-2)}](https://tex.z-dn.net/?f=%5Cfrac%7Ba%5E%7B3n-1%7Db%5E%7Bn%2B1%7D-4a%5E%7Bn-1%7Db%5E%7Bn%2B1%7D%7D%7B4a%5Enb%5E%7Bn-1%7D-4a%5E%7B2n%7Db%5E%7Bn-1%7D%2Ba%5E%7B3n%7Db%5E%7Bn-1%7D%7D%3D%5Cfrac%7Bb%5E%7Bn%2B1%7D%28a%5E%7B3n-1%7D-4a%5E%7Bn-1%7D%29%7D%7Bb%5E%7Bn-1%7D%284a%5En-4a%5E%7B2n%7D%2Ba%5E%7B3n%7D%29%7D%3D%5C%5C%3D%5Cfrac%7Bb%5E%7Bn%2B1-%28n-1%29%7D%2Aa%5E%7Bn-1%7D%28a%5E%7B2n%7D-4%29%7D%7Ba%5En%284-4a%5En%2Ba%5E%7B2n%7D%29%7D%3D%5Cfrac%7Bb%5E2%2Aa%5E%7Bn-1-n%7D%28a%5En-2%29%28a%5En%2B2%29%7D%7B%28a%5En-2%29%5E2%7D%3D%5C%5C%3D%5Cfrac%7Bb%5E2%2A%28a%5En%2B2%29%7D%7Ba%2A%28a%5En-2%29%7D)
a)
![\frac{x^{3n}-x^ny^{2n}}{3x^{3n}+6x^{2n}y^n+3x^ny^{2n}}=\frac{x^n(x^{2n}-y^{2n})}{3x^n(x^{2n}+2x^ny^n+y^{2n})}=\frac{(x^n-y^n)(x^n+y^n)}{3(x^n+y^n)^2}=\frac{x^n-y^n}{3(x^n+y^n)} \frac{x^{3n}-x^ny^{2n}}{3x^{3n}+6x^{2n}y^n+3x^ny^{2n}}=\frac{x^n(x^{2n}-y^{2n})}{3x^n(x^{2n}+2x^ny^n+y^{2n})}=\frac{(x^n-y^n)(x^n+y^n)}{3(x^n+y^n)^2}=\frac{x^n-y^n}{3(x^n+y^n)}](https://tex.z-dn.net/?f=%5Cfrac%7Bx%5E%7B3n%7D-x%5Eny%5E%7B2n%7D%7D%7B3x%5E%7B3n%7D%2B6x%5E%7B2n%7Dy%5En%2B3x%5Eny%5E%7B2n%7D%7D%3D%5Cfrac%7Bx%5En%28x%5E%7B2n%7D-y%5E%7B2n%7D%29%7D%7B3x%5En%28x%5E%7B2n%7D%2B2x%5Eny%5En%2By%5E%7B2n%7D%29%7D%3D%5Cfrac%7B%28x%5En-y%5En%29%28x%5En%2By%5En%29%7D%7B3%28x%5En%2By%5En%29%5E2%7D%3D%5Cfrac%7Bx%5En-y%5En%7D%7B3%28x%5En%2By%5En%29%7D)
a)
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