Задачи для ОГЭ с ответами и решениями

Алгебраические дроби

перейти к содержанию задачника

1. Укажите выражение, тождественно равное дроби \(\displaystyle\frac{a-2x}{5b+6y}\).  
   1) \(\displaystyle\frac{a+2x}{6y-5b}\); 2) \(\displaystyle\frac{x-2a}{6y-5b}\); 3) \(\displaystyle\frac{2x-a}{-5b-6y}\); 4) \(-\displaystyle\frac{-2x-a}{6y+5b}\)
2. Укажите выражение, тождественно равное дроби \(\displaystyle\frac{3a+2x}{5b-3y}\).
   1) \(\displaystyle\frac{-2x-3a}{-5b+3y}\);  2) \(-\displaystyle\frac{2x-3a}{-3y+5b}\);   3) \(\displaystyle\frac{3x+2a}{-3y-5b}\);  4) \(\displaystyle\frac{3a-2x}{-3y-5b}\).
3.  Сократите дробь \(\displaystyle\frac{2ab}{ab+3a^2}\)
4. Сократите дробь \(-\displaystyle\frac{8ab}{ab-3a^2}\)
5. \(\displaystyle\frac{b^2+9b}{b^2-81}\)
6. \(\displaystyle\frac{b^2+10b}{b^2-100}\)
7. Выполните деление\(\displaystyle\frac{a}{ab-2b^2}:\frac{4a^2}{a^2-4ab+4b^2}\)
8. \(\displaystyle\frac{a}{ab+2b^2}:\frac{4a^2}{a^2+4ab+4b^2}\)
9. \(\displaystyle\frac{a}{ab-5b^2}:\frac{5a^2}{a^2-10ab+25b^2}\)
10. \(\displaystyle\frac{3b^2}{a^2-81b^2}:\frac{b}{a^2-9ab}\)
11. Выполните умножение \(\displaystyle\frac{7a}{a^2-25b^2}\cdot (ab+5b^2)\)
12. Найдите разность \(\displaystyle\frac{1}{7x}-\frac{5x+y}{7xy}\)
13. \(\displaystyle\frac{1}{3x}-\frac{-x+y}{3xy}\)
14. Упростите выражение \(\displaystyle\frac{2a}{a^2-9b^2}-\frac{2}{a-3b}\)
15. \(\displaystyle\frac{30x^2}{5x+11}-6x\)
16. \(\displaystyle\frac{2}{a}-\frac{-2a^2+9b^2}{ab}-\frac{2a}{b}\)
17. \(\displaystyle\frac{2}{a}-\frac{-3a^2-10b^2}{ab}-\frac{3a}{b}\)
18. \((\displaystyle\frac{a}{b}+\frac{25b}{a}+10)\cdot\frac{1}{a+5b}\)
19. \((\displaystyle\frac{16y}{x}-\frac{16x}{y}):(4x+4y)\)
20. \((\displaystyle\frac{16y}{x}-\frac{x}{y}):(4y-x)\)
21. \(\displaystyle\frac{b}{20b-16}:\frac{25b^2}{25b^2-16}\)
22. \(\displaystyle\frac{b}{24b-49}:\frac{9b^2}{9b^2-64}\)
23. \(\displaystyle\frac{3a}{9a^2-15ab}-\frac{5b}{9a^2-25b^2}\)
24. \(\displaystyle\frac{16a^2-36b^2}{(2a+3b)^2}\)
25. \(\displaystyle\frac{x^2-25}{x^2-3x-10}\)
26. \(\displaystyle\frac{x^2-4}{x^2+x-6}\)

перейти к содержанию задачника

Ответы

1. 3
2. 1
3. 3
4. 2
5. \(\displaystyle\frac{b}{b-9}\)
6. \(\displaystyle\frac{b}{b-10}\)
7. \(\displaystyle\frac{a-2b}{4ab}\)
8. \(\displaystyle\frac{a+2b}{4ab}\)
9. \(\displaystyle\frac{a-5b}{5ab}\)
10. \(\displaystyle\frac{3ab}{a+9b}\)
11. \(\displaystyle\frac{7ab}{a-5b}\)
12. \(-\displaystyle\frac{5}{7y}\)
13. \(\displaystyle\frac{1}{3y}\)
14. \(-\displaystyle\frac{6b}{a^2-9b^2}\)
15. \(-\displaystyle\frac{66x}{5x+11}\)
16. \(\displaystyle\frac{2-9b}{a}\)
17. \(\displaystyle\frac{2+10b}{a}\)
18. \(\displaystyle\frac{a+5b}{ab}\)
19. \(\displaystyle\frac{4y-4x}{xy}\)
20. \(\displaystyle\frac{4y+x}{xy}\)
21. \(\displaystyle\frac{5b+4}{100b}\)
22. \(\displaystyle\frac{3b+8}{72b}\)
23. \(\displaystyle\frac{3a}{9a^2-25b^2}\)
24. \(\displaystyle\frac{4(2a-3b)}{2a+3b}\)
25. \(\displaystyle\frac{x+5}{x+2}\)
26. \(\displaystyle\frac{x+2}{x+3}\)