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. \(\frac{3x}{2}\)