Задание 2. Найдите корень уравнения. 1) x-x/18=-34/9; 2) -5+x/3=x+8/6; 3) 7x+2/4+1=5x/3; 4) 16/x+3=-8/11; 5) 5/x+9=-2; 6) 5/x-12=12/x-5.

Решим каждое уравнение по отдельности:

1. $$x-\frac{x}{18} = -\frac{34}{9};$$ $$\frac{18x-x}{18} = -\frac{34}{9};$$ $$\frac{17x}{18} = -\frac{34}{9};$$ $$17x = -\frac{34 \cdot 18}{9};$$ $$17x = -34 \cdot 2;$$ $$17x = -68;$$ $$x = -\frac{68}{17};$$ $$x = -4.$$
2. $$-5 + \frac{x}{3} = \frac{x+8}{6};$$ Умножим обе части уравнения на 6: $$-5 \cdot 6 + \frac{x \cdot 6}{3} = \frac{(x+8) \cdot 6}{6};$$ $$-30 + 2x = x+8;$$ $$2x - x = 8 + 30;$$ $$x = 38.$$
3. $$\frac{7x+2}{4} + 1 = \frac{5x}{3};$$ Умножим обе части уравнения на 12: $$\frac{(7x+2) \cdot 12}{4} + 1 \cdot 12 = \frac{5x \cdot 12}{3};$$ $$3(7x+2) + 12 = 4 \cdot 5x;$$ $$21x + 6 + 12 = 20x;$$ $$21x - 20x = -18;$$ $$x = -18.$$
4. $$\frac{16}{x+3} = -\frac{8}{11};$$ $$16 \cdot 11 = -8(x+3);$$ $$176 = -8x - 24;$$ $$8x = -24 - 176;$$ $$8x = -200;$$ $$x = -\frac{200}{8};$$ $$x = -25.$$
5. $$\frac{5}{x+9} = -2;$$ $$5 = -2(x+9);$$ $$5 = -2x - 18;$$ $$2x = -18 - 5;$$ $$2x = -23;$$ $$x = -\frac{23}{2};$$ $$x = -11.5.$$
6. $$\frac{5}{x-12} = \frac{12}{x-5};$$ $$5(x-5) = 12(x-12);$$ $$5x - 25 = 12x - 144;$$ $$5x - 12x = 25 - 144;$$ $$-7x = -119;$$ $$x = \frac{119}{7};$$ $$x = 17.$$

Ответ: 1) -4; 2) 38; 3) -18; 4) -25; 5) -11.5; 6) 17