37.10
1) ![\frac{3x}{x^{3} - 3x^{2}} = \frac{3x}{x^{2}(x-3)} = \frac{3}{x(x-3)} \frac{3x}{x^{3} - 3x^{2}} = \frac{3x}{x^{2}(x-3)} = \frac{3}{x(x-3)}](https://tex.z-dn.net/?f=%5Cfrac%7B3x%7D%7Bx%5E%7B3%7D%20-%203x%5E%7B2%7D%7D%20%3D%20%5Cfrac%7B3x%7D%7Bx%5E%7B2%7D%28x-3%29%7D%20%3D%20%5Cfrac%7B3%7D%7Bx%28x-3%29%7D)
x≠0; x≠3 (при этих значениях в знаменателе будет 0)
При x = 0 - не существует (в знаменателе будет 0)
При x = 0,5: ![\frac{3}{0,5(0,5-3)} = \frac{3}{0,5*(-2,5)} = \frac{3}{-1,25} = -2,4 \frac{3}{0,5(0,5-3)} = \frac{3}{0,5*(-2,5)} = \frac{3}{-1,25} = -2,4](https://tex.z-dn.net/?f=%5Cfrac%7B3%7D%7B0%2C5%280%2C5-3%29%7D%20%3D%20%5Cfrac%7B3%7D%7B0%2C5%2A%28-2%2C5%29%7D%20%3D%20%5Cfrac%7B3%7D%7B-1%2C25%7D%20%3D%20-2%2C4)
При x = 2: ![\frac{3}{2(2-3)} = \frac{3}{-2} = -1,5 \frac{3}{2(2-3)} = \frac{3}{-2} = -1,5](https://tex.z-dn.net/?f=%5Cfrac%7B3%7D%7B2%282-3%29%7D%20%3D%20%5Cfrac%7B3%7D%7B-2%7D%20%3D%20-1%2C5)
При x = 4,6: ![\frac{3}{4,6(4,6-3)} = \frac{3}{4,6*1,6} = \frac{3}{7,36} = \frac{300}{736} = \frac{75}{184} \frac{3}{4,6(4,6-3)} = \frac{3}{4,6*1,6} = \frac{3}{7,36} = \frac{300}{736} = \frac{75}{184}](https://tex.z-dn.net/?f=%5Cfrac%7B3%7D%7B4%2C6%284%2C6-3%29%7D%20%3D%20%5Cfrac%7B3%7D%7B4%2C6%2A1%2C6%7D%20%3D%20%5Cfrac%7B3%7D%7B7%2C36%7D%20%3D%20%5Cfrac%7B300%7D%7B736%7D%20%3D%20%5Cfrac%7B75%7D%7B184%7D)
При x = 3 - не существует (в знаменателе будет 0)
2) ![\frac{2c-3}{2c^{3}-3c^{2}} = \frac{2c-3}{c^{2}(2c-3)} = \frac{1}{c^{2}} \frac{2c-3}{2c^{3}-3c^{2}} = \frac{2c-3}{c^{2}(2c-3)} = \frac{1}{c^{2}}](https://tex.z-dn.net/?f=%5Cfrac%7B2c-3%7D%7B2c%5E%7B3%7D-3c%5E%7B2%7D%7D%20%3D%20%5Cfrac%7B2c-3%7D%7Bc%5E%7B2%7D%282c-3%29%7D%20%3D%20%5Cfrac%7B1%7D%7Bc%5E%7B2%7D%7D)
x≠0
При c = -2: ![\frac{1}{(-2)^{2}} = \frac{1}{4} = 0,25 \frac{1}{(-2)^{2}} = \frac{1}{4} = 0,25](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B%28-2%29%5E%7B2%7D%7D%20%3D%20%5Cfrac%7B1%7D%7B4%7D%20%3D%200%2C25)
При с = 4,5: ![\frac{1}{4,5^{2}} = \frac{1}{20,25} = \frac{100}{2025} = \frac{4}{81} \frac{1}{4,5^{2}} = \frac{1}{20,25} = \frac{100}{2025} = \frac{4}{81}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B4%2C5%5E%7B2%7D%7D%20%3D%20%5Cfrac%7B1%7D%7B20%2C25%7D%20%3D%20%5Cfrac%7B100%7D%7B2025%7D%20%3D%20%5Cfrac%7B4%7D%7B81%7D)
При с =
: ![\frac{1}{(6\frac{1}{4})^{2}} = \frac{1}{(3\frac{1}{2})^{2}} = \frac{1}{9\frac{1}{4}} = \frac{4}{9} \frac{1}{(6\frac{1}{4})^{2}} = \frac{1}{(3\frac{1}{2})^{2}} = \frac{1}{9\frac{1}{4}} = \frac{4}{9}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B%286%5Cfrac%7B1%7D%7B4%7D%29%5E%7B2%7D%7D%20%3D%20%5Cfrac%7B1%7D%7B%283%5Cfrac%7B1%7D%7B2%7D%29%5E%7B2%7D%7D%20%3D%20%5Cfrac%7B1%7D%7B9%5Cfrac%7B1%7D%7B4%7D%7D%20%3D%20%5Cfrac%7B4%7D%7B9%7D)
При с =
: ![\frac{1}{(\frac{2}{3})^{2}} = \frac{1}{\frac{4}{9}} = \frac{9}{4} = 2\frac{1}{4} \frac{1}{(\frac{2}{3})^{2}} = \frac{1}{\frac{4}{9}} = \frac{9}{4} = 2\frac{1}{4}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B%28%5Cfrac%7B2%7D%7B3%7D%29%5E%7B2%7D%7D%20%3D%20%5Cfrac%7B1%7D%7B%5Cfrac%7B4%7D%7B9%7D%7D%20%3D%20%5Cfrac%7B9%7D%7B4%7D%20%3D%202%5Cfrac%7B1%7D%7B4%7D)
При c = 1,5: ![\frac{1}{(1,5)^{2}} = \frac{1}{(\frac{3}{2})^{2}} = \frac{1}{\frac{9}{4}} = \frac{4}{9} \frac{1}{(1,5)^{2}} = \frac{1}{(\frac{3}{2})^{2}} = \frac{1}{\frac{9}{4}} = \frac{4}{9}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B%281%2C5%29%5E%7B2%7D%7D%20%3D%20%5Cfrac%7B1%7D%7B%28%5Cfrac%7B3%7D%7B2%7D%29%5E%7B2%7D%7D%20%3D%20%5Cfrac%7B1%7D%7B%5Cfrac%7B9%7D%7B4%7D%7D%20%3D%20%5Cfrac%7B4%7D%7B9%7D)
37.12
- верно.
- верно.
- неверно.