Райхмист §5 Алгебраические дроби 2.101-2.130

§ 5. Алгебраические дроби

Задачи 2.101 - 2.130 с ответами

Райхмист

Содержание задачника

Упростите выражение:

2.101 \displaystyle\frac{a^3+3a^2b+3ab^2+b^3}{a^2-b^2}
2.102 \displaystyle\frac{(a^2-b^2)(a^2-ab+b^2)}{a-b}
2.103 \displaystyle\frac{a^3-3a^2b+3ab^2-b^3}{a-b}
2.104 \displaystyle\frac{a^3+3a^2b+3ab^2+b^3}{a+b}
2.105 \displaystyle\frac{(a+b)(a^2-ab+b^2)}{b^2-a^2}
2.106 \displaystyle\frac{(a^2-b^2)(a^2+ab+b^2)}{a+b}
2.107 \displaystyle\frac{a^3-3a^2b+3ab^2-b^3}{a-b}
2.108 \displaystyle\frac{(a+b)(a^2-ab+b^2)}{a^2-b^2}
2.109 \displaystyle\frac{a^3-3a^2b+3ab^2-b^3}{a^2-b^2}
2.110 \displaystyle\frac{a^3+3a^2b+3ab^2+b^3}{b^2-a^2}

Выполните действия:

2.111 \displaystyle\frac{a^2+4a+2}{a}-a-\frac{2}{a}
2.112 \displaystyle\frac{b^2+2b-3}{b-1}-b
2.113 \displaystyle\frac{m^2-4m+5}{m-1}-\frac{2}{m-1}-m
2.114 \displaystyle\frac{a+1}{a^2-a-2}-\frac{1}{a-2}
2.115 \displaystyle n-\frac{2}{3n+1}-\frac{3n^2-0,5n-2,5}{3n+1}
2.116 \displaystyle\frac{6b^2-b-2}{3b-2}-2b
2.117 \displaystyle\frac{3a^2+12a+13}{3a+6}-a-\frac{1}{3(a+2)}
2.118 \displaystyle\frac{3m^2-2m-1}{m}-3m+\frac{1}{m}
2.119 \displaystyle\frac{2n^2+11n+14}{n+3}-2n+\frac{1}{n+3}
2.120 \displaystyle\frac{2a^2+5a-12}{2a-3}-a+1

Выполните действия:

2.121 \displaystyle\frac{x}{a^2+ax}+\frac{1}{a+x}
2.122 \displaystyle\frac{a^2-b^2}{a-b}-\frac{a^3-b^3}{a^2-b^2}
2.123 \displaystyle\frac{1}{1-15a^2}+\frac{1}{25a^2-10a+1}
2.124 \displaystyle\frac{x}{x^2+y^2}-\frac{y(x-y)^2}{x^4-y^4}
2.125 \displaystyle\frac{1}{a^2+ab+b^2}+\frac{a+b}{a^3-b^3}
2.126 \displaystyle\frac{1}{x^2+3xy}+\frac{1}{9y^2-x^2}
2.127 \displaystyle\frac{c}{4c^2-9}-\frac{1}{4c+6}
2.128 \displaystyle\frac{x+2}{x^2-2x}-\frac{x-2}{x^2+2x}
2.129 \displaystyle\frac{1}{a^2+2ax}+\frac{1}{2ax+4x^2}
2.130 \displaystyle\frac{a}{a-b}+\frac{a^2b+ab^2}{b^3-a^3}

Ответы

2.101 \frac{(a+b)^2}{a-b}
2.102 a^3+b^3
2.103 (a-b)^2
2.104 (a+b)^2
2.105 \frac{a^2+b^2-ab}{b-a}
2.106 a^3-b^3
2.107 (a-b)^2
2.108 \frac{a^2-ab+b^2}{a-b}
2.109 \frac{(a-b)^2}{a+b}
2.110 \frac{(a+b)^2}{b-a}
2.111 4
2.112 3
2.113 -3
2.114 0
2.115 0,5
2.116 1
2.117 2
2.118 -2
2.119 5
2.120 5
2.121 \frac{1}{a}
2.122 \frac{ab}{a+b}
2.123 \frac{2}{(1-5a)^2(1+5a)}
2.124 \frac{1}{x+y}
2.125 \frac{2a}{a^3-b^3}
2.126 \frac{3y}{x(9y^2-x^2)}
2.127 \frac{3}{2(4c^2-9)}
2.128 \frac{8}{x^2-4}
2.129 \frac{1}{2ax}
2.130 \frac{a^3}{a^3-b^3}