Задачи для ОГЭ с ответами и решениями

Алгебраические дроби II

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1. $\displaystyle\frac{(x+y)^2-(x-y)^2}{x}$
2. $\displaystyle\frac{(x+5y)^2-(x-5y)^2}{y}$
3. $\displaystyle\frac{n^3-3n^2}{n^2-9}$
4. $\displaystyle\frac{n^3-7n^2}{n^-49}$
5. $\displaystyle\frac{b}{2a-b}\cdot (\frac{1}{a}-\frac{2}{b})$
6.  $\displaystyle\frac{a}{5a-7b}\cdot (\frac{7}{a}-\frac{5}{b})$
7. $\displaystyle\frac{x^3+729}{x-6}\cdot\frac{x^2-18x+81}{x^2-9x+81}$
8. $\displaystyle\frac{x^3-343}{x+7}\cdot\frac{x^2+14x+49}{x^2+7x+49}$
9. $\displaystyle\frac{8b^3+12b^2+6b+1}{b}:(\frac{1}{b}+2)$
10. Найдите значение выражения $\displaystyle\frac{6ab}{6ab-6a^2}$ при $a=4, b=6$
11. $\displaystyle\frac{b^2+9b}{b^2-81}$ при $b=11$
12. $\displaystyle\frac{x^2-y^2}{x^2-2xy+y^2}$ при $x=13,5$ и $y=-6,5$
13. $\displaystyle\frac{x^2-25y^2}{x^2-10xy+25y^2}$ при $x=2,6$ и $y=-1,48$
14. $\displaystyle\frac{5a-4b}{ab}-\frac{5}{b}$ при $a=\displaystyle\frac{16}{5}$ и $b=\sqrt{80}$
15. $\displaystyle\frac{6a}{4a^2-b^2}-\frac{3}{2a+b}$ при $a=5$ и $b=5$
16. $\displaystyle\frac{1}{5a}-\frac{25a^2-64}{40a}+\frac{5a}{8}$ при $a=\displaystyle\frac{1}{3}$
17. $\displaystyle\frac{n^3+\sqrt{21}n^2}{n^2-21}$ при $n=2\sqrt{21}$
18. $\displaystyle\frac{a}{5a-1}:\frac{a^2}{25a^2-10a+1}$ при $a=\displaystyle\frac{1}{6}$
19. $\displaystyle\frac{a}{9a-1}:\frac{a^2}{81a^2-18a+1}$ при $a=\displaystyle\frac{1}{6}$
20. $\displaystyle\frac{a^2-16}{a^2}\cdot\frac{a}{a-4}$ при $a=\displaystyle\frac{1}{20}$
21. $(\displaystyle\frac{2y}{x}-\frac{x}{2y}):(2y+x)$ при $x=\displaystyle\frac{1}{6}$ и $y=\displaystyle\frac{1}{9}$
22. $(4u-4v+\displaystyle\frac{v^2}{u}):(2-\frac{v}{u})$ при $u=5+3\sqrt{3}$ и $v=6\sqrt{3}-5$
23. $(4u-12v+\displaystyle\frac{9v^2}{u}):(2-\frac{3v}{u})$ при $u=1+3\sqrt{7}$ и $v=2+2\sqrt{7}$
24. $(a^2+12a+\displaystyle\frac{64}{a}+48)\cdot\frac{1}{a^2-16}\cdot (a^2-4a)$ при $a=-5,5$
25. $(\displaystyle\frac{x}{y}+\frac{9y}{x}-6)\cdot\frac{1}{(x-3y)^2}$ при $x=\sqrt{5}$ и $y=\sqrt{0,2}$
26. $(x+1+\displaystyle\frac{1}{4x}):(x-\frac{1}{4x})$ при $x=11,5$
27. $\displaystyle\frac{5a}{25a^2-30ab}-\frac{6b}{25a^2-36b^2}$ при $a=-8$ и $b=3\sqrt{5}$
28. $\displaystyle\frac{(9x+y)^2-(9x-y)^2}{x}$ при $x=\sqrt{29}$ и $y=-5$

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Ответы

1. $4y$
2. $20x$
3. $\displaystyle\frac{n^2}{n+3}$
4. $\displaystyle\frac{n^2}{n+7}$
5. $-\displaystyle\frac{1}{a}$
6. $-\displaystyle\frac{1}{b}$
7. $x^2-81$
8. $x^2-49$
9. $(2b+1)^2$
10. 3
11. 5,5
12. 0,35
13. -0,48
14. -1,25
15. 0,2
16. 5,4
17. $4\sqrt{21}$
18. -1
19. 3
20. 81
21. 1,5
22. 15
23. -4
24. 2,25
25. 1
26. $\displaystyle\frac{12}{11}$
27. 2
28. -180