Задание 8. Выполните действия: А: 1) 1/2 + x/3; 2) 2/5 + a/2; 3) y/7 − x/3; 4) 2/a + 1/3; 5) x/y + 2/3; 6) 5/a + 1/b; 7) c/7 − 2/a; 8) 8/b − a/c; 9) ab/x − y/3; 10) 3x/a + 2y/b. Б: 1) a/4 + b/8; 2) n/10 − m/5; 3) 6/25 + a/100; 4) 1/(2a) + 1/(2b); 5) 1/(6x) − 1/(6y); 6) 3/(5c) − 2/(15c); 7) x/(3a) + 3x/(6a); 8) a/(28m) − a/(7m); 9) b/(10x) + a/(15x); 10) 5x/(12a) − 2y/(9a). В: 1) 2/(5a) + 1/(6b); 2) 1/(7c) − 1/(5d); 3) 5/(8x) + 1/(12y); 4) 11/(12k) − 5/(18c); 5) a/(6x) + 4/(9xy); 6) 3/(20bc) − x/(15c); 7) 3/(ab) + 2/(ac); 8) 1/(xy) − 1/(xz); 9) 2/(ab) − 2/(cx); 10) 5/(abx) + 2/(acy). Г: 1) 5/x + 2/x²; 2) 8/a³ − 3/a; 3) 5/x³ + a/x²; 4) 1/b⁵ + c/b³; 5) 4/(3a) + 5/a²; 6) x/(8c²) − 5/(12c); 7) 9/(10b²) − 8/(2b³); 8) a/(16n²) + b/(24n³); 9) y/(12c⁴) + x/(18c⁶); 10) 5/(ab⁷) − 3/(cb⁵).

Приводим дроби к общему знаменателю и объединяем числители.

А

1. \(\frac{1}{2}+\frac{x}{3}=\frac{3+2x}{6}\).
2. \(\frac{2}{5}+\frac{a}{2}=\frac{4+5a}{10}\).
3. \(\frac{y}{7}-\frac{x}{3}=\frac{3y-7x}{21}\).
4. \(\frac{2}{a}+\frac{1}{3}=\frac{6+a}{3a}\).
5. \(\frac{x}{y}+\frac{2}{3}=\frac{3x+2y}{3y}\).
6. \(\frac{5}{a}+\frac{1}{b}=\frac{5b+a}{ab}\).
7. \(\frac{c}{7}-\frac{2}{a}=\frac{ac-14}{7a}\).
8. \(\frac{8}{b}-\frac{a}{c}=\frac{8c-ab}{bc}\).
9. \(\frac{ab}{x}-\frac{y}{3}=\frac{3ab-xy}{3x}\).
10. \(\frac{3x}{a}+\frac{2y}{b}=\frac{3bx+2ay}{ab}\).

Б

1. \(\frac{a}{4}+\frac{b}{8}=\frac{2a+b}{8}\).
2. \(\frac{n}{10}-\frac{m}{5}=\frac{n-2m}{10}\).
3. \(\frac{6}{25}+\frac{a}{100}=\frac{24+a}{100}\).
4. \(\frac{1}{2a}+\frac{1}{2b}=\frac{a+b}{2ab}\).
5. \(\frac{1}{6x}-\frac{1}{6y}=\frac{y-x}{6xy}\).
6. \(\frac{3}{5c}-\frac{2}{15c}=\frac{7}{15c}\).
7. \(\frac{x}{3a}+\frac{3x}{6a}=\frac{5x}{6a}\).
8. \(\frac{a}{28m}-\frac{a}{7m}=-\frac{3a}{28m}\).
9. \(\frac{b}{10x}+\frac{a}{15x}=\frac{3b+2a}{30x}\).
10. \(\frac{5x}{12a}-\frac{2y}{9a}=\frac{15x-8y}{36a}\).

В

1. \(\frac{2}{5a}+\frac{1}{6b}=\frac{12b+5a}{30ab}\).
2. \(\frac{1}{7c}-\frac{1}{5d}=\frac{5d-7c}{35cd}\).
3. \(\frac{5}{8x}+\frac{1}{12y}=\frac{15y+2x}{24xy}\).
4. \(\frac{11}{12k}-\frac{5}{18c}=\frac{33c-10k}{36kc}\).
5. \(\frac{a}{6x}+\frac{4}{9xy}=\frac{3ay+8}{18xy}\).
6. \(\frac{3}{20bc}-\frac{x}{15c}=\frac{9-4bx}{60bc}\).
7. \(\frac{3}{ab}+\frac{2}{ac}=\frac{3c+2b}{abc}\).
8. \(\frac{1}{xy}-\frac{1}{xz}=\frac{z-y}{xyz}\).
9. \(\frac{2}{ab}-\frac{2}{cx}=\frac{2cx-2ab}{abcx}\).
10. \(\frac{5}{abx}+\frac{2}{acy}=\frac{5cy+2bx}{abcxy}\).

Г

1. \(\frac{5}{x}+\frac{2}{x^2}=\frac{5x+2}{x^2}\).
2. \(\frac{8}{a^3}-\frac{3}{a}=\frac{8-3a^2}{a^3}\).
3. \(\frac{5}{x^3}+\frac{a}{x^2}=\frac{5+ax}{x^3}\).
4. \(\frac{1}{b^5}+\frac{c}{b^3}=\frac{1+cb^2}{b^5}\).
5. \(\frac{4}{3a}+\frac{5}{a^2}=\frac{4a+15}{3a^2}\).
6. \(\frac{x}{8c^2}-\frac{5}{12c}=\frac{3x-10c}{24c^2}\).
7. \(\frac{9}{10b^2}-\frac{8}{2b^3}=\frac{9b-40}{10b^3}\).
8. \(\frac{a}{16n^2}+\frac{b}{24n^3}=\frac{3an+2b}{48n^3}\).
9. \(\frac{y}{12c^4}+\frac{x}{18c^6}=\frac{3yc^2+2x}{36c^6}\).
10. \(\frac{5}{ab^7}-\frac{3}{cb^5}=\frac{5c-3ab^2}{acb^7}\).