§ 5. Алгебраические дроби

Задачи 2.101 - 2.130 с ответами

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 $\frac{a^3}{a^3-b^3}$