![\frac{18x+36}{4x^{2}-64}=\frac{18(x+2)}{4(x^{2}-16)}](https://tex.z-dn.net/?f=%5Cfrac%7B18x%2B36%7D%7B4x%5E%7B2%7D-64%7D%3D%5Cfrac%7B18%28x%2B2%29%7D%7B4%28x%5E%7B2%7D-16%29%7D)
Теперь решим систему, числитель равен нулю, знаменатель не равен
![\left \{ {{18(x+2)=0} \atop {4(x^{2}-16)\neq 0}} \right.](https://tex.z-dn.net/?f=%5Cleft%20%5C%7B%20%7B%7B18%28x%2B2%29%3D0%7D%20%5Catop%20%7B4%28x%5E%7B2%7D-16%29%5Cneq%200%7D%7D%20%5Cright.)
![18(x+2)=0\\x+2=0\\x=-2](https://tex.z-dn.net/?f=18%28x%2B2%29%3D0%5C%5Cx%2B2%3D0%5C%5Cx%3D-2)
![4(x^{2}-16)\neq 0\\x^{2}-16\neq 0\\(x-4)(x+4)\neq 0\\\\x\neq 4\\x\neq -4](https://tex.z-dn.net/?f=4%28x%5E%7B2%7D-16%29%5Cneq%200%5C%5Cx%5E%7B2%7D-16%5Cneq%200%5C%5C%28x-4%29%28x%2B4%29%5Cneq%200%5C%5C%5C%5Cx%5Cneq%204%5C%5Cx%5Cneq%20-4)
Получаем точки -4 -2 4
Область определения или D(f)=(-∞;-4)∪(-4;2]∪[2;4)∪(4;+∞)
Пусть скорость течения реки х м\мин, собственная скорость лодки(скорость с которой гребли туристы) равна y м\мин, тогда сокрость лодки по течению реки равна x+y м\мин, против течения реки y-x м\мин/ По условию задачи составляем уравнение(расстояние которые туристы проплыли против течения реки равно расстоянию которое они сложили весла и плыли против течения):
<h2>4. <u>Решить уравнение</u>.</h2>
![(3x^2 + 9x - 5) - (7x^2 - 6x + 2) = 7 - 2x - 4x^2;](https://tex.z-dn.net/?f=%283x%5E2+%2B+9x+-+5%29+-+%287x%5E2+-+6x+%2B+2%29+%3D+7+-+2x+-+4x%5E2%3B)
![3x^2 + 9x - 5 - 7x^2 + 6x - 2 = 7 - 2x - 4x^2;](https://tex.z-dn.net/?f=3x%5E2+%2B+9x+-+5+-+7x%5E2+%2B+6x+-+2+%3D+7+-+2x+-+4x%5E2%3B)
![(3x^2 - 7x^2) + (9x + 6x) - 5 - 2 = 7 - 2x - 4x^2;](https://tex.z-dn.net/?f=%283x%5E2+-+7x%5E2%29+%2B+%289x+%2B+6x%29+-+5+-+2+%3D+7+-+2x+-+4x%5E2%3B)
![-4x^2 + 15x - 7 = 7 - 2x - 4x^2;](https://tex.z-dn.net/?f=-4x%5E2+%2B+15x+-+7+%3D+7+-+2x+-+4x%5E2%3B)
![15x - 7 = 7 - 2x;](https://tex.z-dn.net/?f=15x+-+7+%3D+7+-+2x%3B)
![15x + 2x = 7 + 7;](https://tex.z-dn.net/?f=15x+%2B+2x+%3D+7+%2B+7%3B)
![17x = 14;](https://tex.z-dn.net/?f=17x+%3D+14%3B)
![x = \frac{14}{17}.](https://tex.z-dn.net/?f=x+%3D+%5Cfrac%7B14%7D%7B17%7D.)
<u>Ответ</u>:
.
<h2>5. <u>Вычислить</u>.</h2>
1) ![\frac{216^5*36^3}{6^{20}} = \frac{(6^3)^5*(6^2)^3}{6^{20}} = \frac{6^{15}*6^6}{6^{20}} = \frac{6^{15+6}}{6^{20}} = \frac{6^{21}}{6^{20}} = 6^{21-20} = 6^1 = 6.](https://tex.z-dn.net/?f=%5Cfrac%7B216%5E5%2A36%5E3%7D%7B6%5E%7B20%7D%7D+%3D+%5Cfrac%7B%286%5E3%29%5E5%2A%286%5E2%29%5E3%7D%7B6%5E%7B20%7D%7D+%3D+%5Cfrac%7B6%5E%7B15%7D%2A6%5E6%7D%7B6%5E%7B20%7D%7D+%C2%A0%3D+%5Cfrac%7B6%5E%7B15%2B6%7D%7D%7B6%5E%7B20%7D%7D+%3D+%5Cfrac%7B6%5E%7B21%7D%7D%7B6%5E%7B20%7D%7D+%3D+6%5E%7B21-20%7D+%3D+6%5E1+%3D+6.)
2) ![\frac{18^{14}}{6^{12}*3^{14}} = \frac{(2*3^2)^{14}}{(2*3)^{12}*3^{14}} = \frac{2^{14}*(3^2)^{14}}{2^{12}*3^{12}*3^{14}} = \frac{2^{14}*3^{28}}{2^{12}*3^{12+14}} = \frac{2^{14}*3^{28}}{2^{12}*3^{26}} =\\= 2^{14-12}*3^{28-26} = 2^2*3^2 = 4*9 = 36.](https://tex.z-dn.net/?f=%5Cfrac%7B18%5E%7B14%7D%7D%7B6%5E%7B12%7D%2A3%5E%7B14%7D%7D+%3D+%5Cfrac%7B%282%2A3%5E2%29%5E%7B14%7D%7D%7B%282%2A3%29%5E%7B12%7D%2A3%5E%7B14%7D%7D+%3D+%5Cfrac%7B2%5E%7B14%7D%2A%283%5E2%29%5E%7B14%7D%7D%7B2%5E%7B12%7D%2A3%5E%7B12%7D%2A3%5E%7B14%7D%7D+%3D+%5Cfrac%7B2%5E%7B14%7D%2A3%5E%7B28%7D%7D%7B2%5E%7B12%7D%2A3%5E%7B12%2B14%7D%7D+%3D+%5Cfrac%7B2%5E%7B14%7D%2A3%5E%7B28%7D%7D%7B2%5E%7B12%7D%2A3%5E%7B26%7D%7D+%3D%5C%5C%3D+2%5E%7B14-12%7D%2A3%5E%7B28-26%7D+%3D+2%5E2%2A3%5E2+%3D+4%2A9+%3D+36.)
3) ![(\frac{6}{11})^9*(1\frac{5}{6})^7 = (\frac{6}{11})^9*(\frac{11}{6})^7 = (\frac{6}{11})^9*(\frac{6}{11})^{-7 } = (\frac{6}{11})^{9+(-7)} =\\= (\frac{6}{11})^{9-7} = (\frac{6}{11})^2 = \frac{6^2}{11^2} = \frac{36}{121}.](https://tex.z-dn.net/?f=%28%5Cfrac%7B6%7D%7B11%7D%29%5E9%2A%281%5Cfrac%7B5%7D%7B6%7D%29%5E7+%3D+%28%5Cfrac%7B6%7D%7B11%7D%29%5E9%2A%28%5Cfrac%7B11%7D%7B6%7D%29%5E7+%3D+%28%5Cfrac%7B6%7D%7B11%7D%29%5E9%2A%28%5Cfrac%7B6%7D%7B11%7D%29%5E%7B-7+%7D+%3D+%28%5Cfrac%7B6%7D%7B11%7D%29%5E%7B9%2B%28-7%29%7D+%3D%5C%5C%3D+%28%5Cfrac%7B6%7D%7B11%7D%29%5E%7B9-7%7D+%3D+%28%5Cfrac%7B6%7D%7B11%7D%29%5E2+%3D+%5Cfrac%7B6%5E2%7D%7B11%5E2%7D+%3D+%5Cfrac%7B36%7D%7B121%7D.)
<u>Ответ</u>: 6; 36;
.
<h2>
6. <u>
Найти (*)</u>
.</h2>
![(5x^2 - 3xy - y^2) - (*) = x^2 + 3xy;](https://tex.z-dn.net/?f=%285x%5E2+-+3xy+-+y%5E2%29+-+%28%2A%29+%3D+x%5E2+%2B+3xy%3B)
![(*) = (5x^2 - 3xy - y^2) - (x^2 + 3xy);](https://tex.z-dn.net/?f=%28%2A%29+%3D+%285x%5E2+-+3xy+-+y%5E2%29+-+%28x%5E2+%2B+3xy%29%3B)
![(*) = 5x^2 - 3xy - y^2 - x^2 - 3xy;](https://tex.z-dn.net/?f=%28%2A%29+%3D+5x%5E2+-+3xy+-+y%5E2+-+x%5E2+-+3xy%3B)
![(*) = 4x^2 - 6xy - y^2.](https://tex.z-dn.net/?f=%28%2A%29+%3D+4x%5E2+-+6xy+-+y%5E2.)
<u>Ответ</u>: 4x² - 6xy - y².
1. х+3у=2
x=2-3y
2.2x+3y=7
2(2-3y)=7
4-6y=7
-6y=7-4
-6y=-3
y=0.5
Потом: x+3y=2------x+3*0.5=2--------x+1.5=2-----x=2-1.5------x=0.5
Ответ: х=0,5. у=0,5.