§ 5. Алгебраические дроби
Задачи 2.101 – 2.130 с ответами
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 \(\frac{a^3}{a^3-b^3}\)