1. \(\quad3x-1=4x+2\)
2. \(\quad\displaystyle\frac{1}{x-3}-\frac{1}{x+6}=\frac{9}{x^2+3x-18}\)
3. \(\quad x^4+7x^2-18=0\)
4. \(\quad6x^2-7x+1=0\)
5. \(\quad\) Найдите все значения переменной, при которых разность дробей \(\displaystyle\frac{x-3}{x-2}\) и \(\displaystyle\frac{3}{x+1}\) равна дроби \(\displaystyle\frac{3}{x^2-x-2}\).
6. \(\quad\displaystyle\frac{x-1}{2}=\frac{2x+4}{3}\)
7. \(\quad6x^2+x=0\)
8. \(\quad\displaystyle\frac{x}{x+4}-\frac{2}{x-4}+\frac{16}{x^2-16}=0\)
9. \(\quad1-\displaystyle\frac{3x^2-x-24}{3-x}=0\)
10. \(\quad\displaystyle\frac{2x}{x^2-36}+\frac{5-x}{x-6}=0\)
11. \(\quad(x+4)^2-(x-8)^2=32\)
12. \(\quad(x^2-5x+2)(x^2-5x-4)=-9\)
13. \(\quad\displaystyle\frac{5x-1}{3}-\frac{2x+3}{5}=1\)
14. \(\quad x^4-8x^2-9=0\)
15. \(\quad\displaystyle\frac{2x+5}{2}-\frac{x^2+10x}{10}=1\)
16. \(\quad(x^2+3x)^2-14x^2-42x+40=0\)
17. \(\quad(2x-3)(x+1)=x^2+9\)
18. \(\quad\displaystyle\frac{2x-7}{x^2-9x+14}-\frac{1}{x-1}=\frac{1}{x^2-3x+2}\)
19. \(\quad\displaystyle\frac{3}{x-2}+1=\frac{10}{x^2-4x+4}\)
20. \(\quad\displaystyle\frac{x}{x+2}-\frac{6}{x-2}+\frac{24}{x^2-4}=0\)
21. \(\quad\displaystyle\frac{x+2}{x-1}+\frac{x+3}{x+1}=\frac{x+5}{x^2-1}\)
22. \(\quad\displaystyle\frac{5}{6+x-x^2}-1=\frac{1}{x+2}\)
23. \(\quad\) Пусть \(x_1\) и \(x_2\) – корни уравнения \(x^2+13x-15=0\). Найдите значение выражения \(\displaystyle\frac{x^2_1+x^2_2}{4x_1x_2}\)

Ответы

1. -3
2. \((-\infty;-6)\cup(-6;3)\cup(3;+\infty)\)
3. \(\pm\sqrt{2}\)
4. 1/6;1
5. 0;5
6. -11
7. -1/6;0
8. 2
9. -3
10. -5
11. 10/3
12. \((5\pm\sqrt{29})/2\)
13. 29/19
14. -3;3
15. \(\pm\sqrt{15}\)
16. -5;-4;1;2
17. -3;4
18. 0
19. -3;4
20. 6
21. -3
22. 2
23. -199/60