Задачи по школьной математике. Преобразование выражений IV

Преобразование выражений

  1. \displaystyle \frac{x+3}{x^2+9}\cdot\left(\frac{x+3}{x-3}+\frac{x-3}{x+3}\right)
  2. \displaystyle \frac{4xy}{y^2-x^2}:\left(\frac{1}{y^2-x^2}+\frac{1}{x^2+2xy+y^2}\right)
  3. \displaystyle \left(\frac{x-2y}{x+2xy}-\frac{1}{x^2-4y^2}:\frac{x+2y}{(2y-x)^2}\right)\cdot\frac{(x+2y)^2}{4y^2}
  4. \displaystyle 1-\left(\frac{2}{a-2}-\frac{2}{a+2}\right)\cdot\left(a-\frac{3a+2}{4}\right)
  5. \displaystyle \left(\frac{2a}{2a+b}-\frac{4a^2}{4a^2+4ab+b^2}\right):\left(\frac{2a}{4a^2-b^2}+\frac{1}{b-2a}\right)
  6. \displaystyle \left(\frac{1}{a-c}-\frac{3c^2}{a^3-c^3}-\frac{c}{a^2+ac+c^2}\right)\cdot\left(c+\frac{a^2}{a+c}\right)
  7. \displaystyle\frac{b-c}{b}-\frac{b}{b+c}
  8. \displaystyle \frac{x+1}{x-2}-\frac{x+3}{x}
  9. \displaystyle \frac{2a}{2a-1}-\frac{1}{2a+1}
  10. \displaystyle \frac{a}{7a-14}+\frac{1}{2-a}
  11. \displaystyle \frac{a^2-1}{a-b}\cdot\frac{7a-7b}{a^2+a}
  12. \displaystyle \frac{(y-5)^2}{2y+12}\cdot\frac{y^2-36}{2y-10}
  13. \displaystyle \frac{a^2+6a+9}{a^3+27}\cdot\frac{a^2-3a+9}{3a+9}
  14. \displaystyle \frac{x^3-y^3}{x+y}\cdot\frac{x^2-y^2}{x^2+xy+y^2}
  15. \displaystyle \frac{a^2+3a}{ab-5b+8a-40}-\frac{a}{b+8}
  16. \displaystyle \frac{y}{3x-2}-\frac{3y}{6xy+9x-4y-6}
  17. \displaystyle \frac{a-2y}{a+y}-\frac{y^2-5ay}{a^2-y^2}
  18. \displaystyle \frac{a+3}{a^2-1}-\frac{1}{a^2+a}
  19. \displaystyle \frac{b-6}{4-b^2}+\frac{2}{2b-b^2}
  20. \displaystyle \frac{b}{ab-5a^2}-\frac{15b-25a}{b^2-25a^2}
  21. \displaystyle \frac{x-12a}{x^2-16a^2}-\frac{4a}{4ax-x^2}
  22. \displaystyle \frac{x^2-4}{5x-10}-\frac{x^2+4x+4}{5x+10}
  23. \displaystyle \frac{x-2}{x^2+2x+4}-\frac{6x}{x^3-8}+\frac{1}{x-2}
  24. \displaystyle \frac{2x^2+16}{x^3+8}-\frac{2}{x+2}
  25. \displaystyle \left(\frac{a-7b}{ab-b^2}+\frac{7a+b}{a^2-ab}\right):\frac{a^2+b^2}{a-b}
  26. \displaystyle (y^2-4)\left(\frac{3}{y+2}-\frac{2}{y-2}\right)+5
  27. \displaystyle \left(1-\frac{9x^2+4}{12x}\right):\left(\frac{1}{3x}-\frac{1}{2}\right)+1

Ответы

  1. \displaystyle \frac{2}{x-3}
  2. \displaystyle 2x^2+2xy
  3. \displaystyle \frac{x-2y}{2xy}
  4. \displaystyle \frac{a}{a+2}
  5. \displaystyle \frac{2ab-4a^2}{2a+b}
  6. 1
  7. -\frac{c^2}{b(b+c)}
  8. \frac{6}{x(x-2)}
  9. \frac{4a^2+1}{4a^2-1}
  10. \frac{a-7}{7(a-2)}
  11. \frac{7(a-1)}{a}
  12. \frac{(y-5)(y-6)}{4}
  13. 1/3
  14. (x-y)^2
  15. \frac{8a}{(b+8)(a-5)}
  16. \frac{2y^2}{(3x-2)(2y+3)}
  17. \frac{a+y}{a-y}
  18. \frac{a+1}{a(a-1)}
  19. \frac{2-b}{b(b+2)}
  20. \frac{b-5a}{a(b+5a)}
  21. \frac{x-4a}{x(x+4a)}
  22. 0
  23. \frac{2(x-2)}{x^2+2x+4}
  24. \frac{4}{x^2-2x+4}
  25. \frac{1}{ab}
  26. y-5
  27. \frac{3x}{2}