(y^(3)-16y) / (2y+18)( (y^(2)+9y) / (4-y))упростить выражение
(5c^(3)-5)/(c+5):((c+1)^(2))-c)/13c+26 -упростить выражение
(0.25a^-3*b^4)^-2*(2a^(5)*b^-6)^-1 упростить выражение
(25*4^n)/(4^n-4^n-1)
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Answers & Comments
1.![\frac{y^3-16y}{2y+18}*\frac{y^2+9y}{4-y}=\frac{y^2(y-4)(y+4)(y+9)}{2(y+9)(4-y)}= \frac{y^3-16y}{2y+18}*\frac{y^2+9y}{4-y}=\frac{y^2(y-4)(y+4)(y+9)}{2(y+9)(4-y)}=](https://tex.z-dn.net/?f=%5Cfrac%7By%5E3-16y%7D%7B2y%2B18%7D%2A%5Cfrac%7By%5E2%2B9y%7D%7B4-y%7D%3D%5Cfrac%7By%5E2%28y-4%29%28y%2B4%29%28y%2B9%29%7D%7B2%28y%2B9%29%284-y%29%7D%3D)
![=\frac{-y^2(y+4)}{2} =\frac{-y^2(y+4)}{2}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B-y%5E2%28y%2B4%29%7D%7B2%7D)
2.![\frac{5c^3-5}{c+5}:\frac{(c+1)^2-c}{13c+26}=\frac{5(c-1)(c^2+c+1)13(c+2)}{(c+5)(c^2+c+1)}=\frac{65(c-1)(c+2)}{c+5} \frac{5c^3-5}{c+5}:\frac{(c+1)^2-c}{13c+26}=\frac{5(c-1)(c^2+c+1)13(c+2)}{(c+5)(c^2+c+1)}=\frac{65(c-1)(c+2)}{c+5}](https://tex.z-dn.net/?f=%5Cfrac%7B5c%5E3-5%7D%7Bc%2B5%7D%3A%5Cfrac%7B%28c%2B1%29%5E2-c%7D%7B13c%2B26%7D%3D%5Cfrac%7B5%28c-1%29%28c%5E2%2Bc%2B1%2913%28c%2B2%29%7D%7B%28c%2B5%29%28c%5E2%2Bc%2B1%29%7D%3D%5Cfrac%7B65%28c-1%29%28c%2B2%29%7D%7Bc%2B5%7D)
3.![(0.25a^{-3}b^4)^{-2}*(2a^5b^{-6})^{-1}=\frac{a^6b^6}{0.25^2b^82a^5}=\frac{8a}{b^2} (0.25a^{-3}b^4)^{-2}*(2a^5b^{-6})^{-1}=\frac{a^6b^6}{0.25^2b^82a^5}=\frac{8a}{b^2}](https://tex.z-dn.net/?f=%280.25a%5E%7B-3%7Db%5E4%29%5E%7B-2%7D%2A%282a%5E5b%5E%7B-6%7D%29%5E%7B-1%7D%3D%5Cfrac%7Ba%5E6b%5E6%7D%7B0.25%5E2b%5E82a%5E5%7D%3D%5Cfrac%7B8a%7D%7Bb%5E2%7D)
4.![\frac{25*4^n}{4^n-4^{n-1}}=\frac{25*4^n}{\frac{3}{4}*4^n}=100/3 \frac{25*4^n}{4^n-4^{n-1}}=\frac{25*4^n}{\frac{3}{4}*4^n}=100/3](https://tex.z-dn.net/?f=%5Cfrac%7B25%2A4%5En%7D%7B4%5En-4%5E%7Bn-1%7D%7D%3D%5Cfrac%7B25%2A4%5En%7D%7B%5Cfrac%7B3%7D%7B4%7D%2A4%5En%7D%3D100%2F3)