Преобразование выражений

1. $\displaystyle \frac{16y}{9x^2+4xy}-\frac{81x}{9xy+4y^2}$
2. $\displaystyle \frac{x-5}{x^2+5x}+\frac{x+5}{x^2-5x}-\frac{4x}{x^2-25}$
3. $\displaystyle \left (\frac{x}{8x+1}+1\right)\cdot\frac{1-64x^2}{81x^2-1}-\frac{8x}{1-9x}$
4. $\displaystyle \left(\frac{5}{3-x}-4x\right):\frac{4x^2-12x+5}{x^2-6x+9}$
5. $\displaystyle \left(4x+1-\frac{1}{1-4x}\right):\left(4x-\frac{16x^2}{4x-1}\right)$
6. $\displaystyle \frac{a+8}{a^2-36}-\frac{1}{a^2-36}\cdot\frac{(a+6)^2}{a}$
7. $\displaystyle \left(\frac{a+b}{a^2+ab}-\frac{1}{a^2-b^2}:\frac{a+b}{(b-a)^2}\right)\cdot\frac{(a+b)^2}{2b^2}$
8. $\displaystyle \left(\frac{9a+c}{a^2-9ac}+\frac{9a-c}{a^2+9ac}\right)\cdot\frac{a^2-81c^2}{a^2+c^2}$
9. $\displaystyle \left(\frac{a^3-27b^3}{a-3b}+3ab\right)\cdot\left(\frac{a-3b}{a^2-9b^2}\right)^2$
10. $\displaystyle \left(\frac{2xy}{y^2-16x^2}-\frac{x}{y-4x}\right):\frac{x^2}{y^2+4xy}$
11. $\displaystyle \left(\frac{a+3b}{a-3b}+\frac{a-3b}{a+3b}-\frac{a^2+9b^2}{a^2-9b^2}\right)\cdot\frac{5a^2-45b^2}{a^2+9b^2}$
12. $\displaystyle \frac{1}{x+y}\cdot\left(\frac{x}{y}-\frac{y}{x}\right)-\frac{2x-y}{xy}+\frac{1}{y}$
13. $\displaystyle \frac{a-a^8}{a^6+a^2}:\frac{a^9-a^2}{a^5+a}$
14. $\displaystyle \frac{x^2-bx+ax-ab}{x^2+bx-ax-ab}:\frac{x^2+bx+ax+ab}{a^2-bx-ax+ab}$
15. $\displaystyle \frac{m^2+m-mn-n}{m^2+m+mn+n}:\frac{m^2-m-mn+n}{m^2-m+mn-n}$
16. $\displaystyle \frac{a^2+ax+ab+bx}{a^2-ax-ab+bx}\cdot\frac{a^2-ax-bx+ab}{a^2+ax-bx-ab}$
17. $\displaystyle \frac{5}{y-3}+\frac{1}{y+3}-\frac{4y-18}{y^2-9}$
18. $\displaystyle \frac{1-x^2}{4x^2-x-3}$
19. $\displaystyle \frac{3-5x-2x^2}{x^2-9}$
20. $\displaystyle \frac{2x^2+x-6}{x^2+2x}$
21. $\displaystyle \frac{x^2-xy-2y^2}{x^2+y^2+2xy}$
22. $\displaystyle \frac{8x^2+10xy-3y^2}{2x^2+xy-3y^2}$

Ответы

1. $\frac{4y-9x}{xy}$
2. $-\frac{2}{x}$
3. $\frac{1}{9x-1}$
4. $3-x$
5. $-4x$
6. $\frac{6}{a(a+6)}$
7. $\frac{3a+b}{2ab}$
8. $\frac{18}{a}$
9. 1
10. $\frac{y}{x}$
11. 5
12. 0
13. $\displaystyle -\frac{1}{a^2}$
14. $\displaystyle \frac{(x-b)^2}{(x+b)^2}$
15. 1
16. $\displaystyle \frac{(a+b)^2}{(a-b)^2}$
17. $\displaystyle \frac{2y+30}{y^2-9}$
18. $\displaystyle -\frac{x+1}{4x+3}$
19. $\displaystyle \frac{1-2x}{x-3}$
20. $\displaystyle \frac{2x-3}{x}$
21. $\displaystyle \frac{x-2y}{x+y}$
22. $\displaystyle \frac{4x-y}{x-y}$