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