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franksterik
@franksterik
March 2022
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д)![\frac{2a+1}{a-7} +(\frac{a}{a+8} +\frac{a}{7-a}) : \frac{a}{8+a} = \frac{2a+1}{a-7} +\frac{a(7-a)+a(a+8)}{(a+8)(7-a)} : \frac{a}{8+a} = \frac{2a+1}{a-7} +\frac{7a-a^2+a^{2} +8a}{(a+8)(7-a)} * \frac{a+8}{a} = \frac{2a+1}{a-7} + \frac{15a}{a(7-a)} = -\frac{2a-1}{7-a} +\frac{15}{7-a} =\frac{-2a-1+15}{7-a} = \frac{14-2a}{7-a} =\frac{2(7-a)}{7-a} =2 \frac{2a+1}{a-7} +(\frac{a}{a+8} +\frac{a}{7-a}) : \frac{a}{8+a} = \frac{2a+1}{a-7} +\frac{a(7-a)+a(a+8)}{(a+8)(7-a)} : \frac{a}{8+a} = \frac{2a+1}{a-7} +\frac{7a-a^2+a^{2} +8a}{(a+8)(7-a)} * \frac{a+8}{a} = \frac{2a+1}{a-7} + \frac{15a}{a(7-a)} = -\frac{2a-1}{7-a} +\frac{15}{7-a} =\frac{-2a-1+15}{7-a} = \frac{14-2a}{7-a} =\frac{2(7-a)}{7-a} =2](https://tex.z-dn.net/?f=%5Cfrac%7B2a%2B1%7D%7Ba-7%7D%20%2B%28%5Cfrac%7Ba%7D%7Ba%2B8%7D%20%2B%5Cfrac%7Ba%7D%7B7-a%7D%29%20%3A%20%5Cfrac%7Ba%7D%7B8%2Ba%7D%20%3D%20%5Cfrac%7B2a%2B1%7D%7Ba-7%7D%20%2B%5Cfrac%7Ba%287-a%29%2Ba%28a%2B8%29%7D%7B%28a%2B8%29%287-a%29%7D%20%3A%20%5Cfrac%7Ba%7D%7B8%2Ba%7D%20%3D%20%5Cfrac%7B2a%2B1%7D%7Ba-7%7D%20%2B%5Cfrac%7B7a-a%5E2%2Ba%5E%7B2%7D%20%2B8a%7D%7B%28a%2B8%29%287-a%29%7D%20%2A%20%5Cfrac%7Ba%2B8%7D%7Ba%7D%20%3D%20%5Cfrac%7B2a%2B1%7D%7Ba-7%7D%20%2B%20%5Cfrac%7B15a%7D%7Ba%287-a%29%7D%20%3D%20-%5Cfrac%7B2a-1%7D%7B7-a%7D%20%2B%5Cfrac%7B15%7D%7B7-a%7D%20%3D%5Cfrac%7B-2a-1%2B15%7D%7B7-a%7D%20%3D%20%5Cfrac%7B14-2a%7D%7B7-a%7D%20%3D%5Cfrac%7B2%287-a%29%7D%7B7-a%7D%20%3D2)
ж)![25\sqrt{b} -0,5\sqrt{4b} +100\sqrt{0,16b} =25\sqrt{b} -0,5*2\sqrt{b} +100\sqrt{\frac{4}{25} b} = 25\sqrt{b} -\sqrt{b} +100*\frac{2}{5} \sqrt{b} =25\sqrt{b} -\sqrt{b} +40\sqrt{b} =(25-1+40)\sqrt{b} =64\sqrt{b} 25\sqrt{b} -0,5\sqrt{4b} +100\sqrt{0,16b} =25\sqrt{b} -0,5*2\sqrt{b} +100\sqrt{\frac{4}{25} b} = 25\sqrt{b} -\sqrt{b} +100*\frac{2}{5} \sqrt{b} =25\sqrt{b} -\sqrt{b} +40\sqrt{b} =(25-1+40)\sqrt{b} =64\sqrt{b}](https://tex.z-dn.net/?f=25%5Csqrt%7Bb%7D%20-0%2C5%5Csqrt%7B4b%7D%20%2B100%5Csqrt%7B0%2C16b%7D%20%3D25%5Csqrt%7Bb%7D%20-0%2C5%2A2%5Csqrt%7Bb%7D%20%2B100%5Csqrt%7B%5Cfrac%7B4%7D%7B25%7D%20b%7D%20%3D%2025%5Csqrt%7Bb%7D%20-%5Csqrt%7Bb%7D%20%2B100%2A%5Cfrac%7B2%7D%7B5%7D%20%5Csqrt%7Bb%7D%20%3D25%5Csqrt%7Bb%7D%20-%5Csqrt%7Bb%7D%20%2B40%5Csqrt%7Bb%7D%20%3D%2825-1%2B40%29%5Csqrt%7Bb%7D%20%3D64%5Csqrt%7Bb%7D)