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1. 计算：$\frac{2a}{5a^2b} + \frac{3b}{10ab^2} = (\quad)$
A.$\frac{1}{2ab}$
B.$\frac{7}{10b}$
C.$\frac{7}{10ab}$
D.$\frac{2a+3b}{10a^2b^2}$
A.$\frac{1}{2ab}$
B.$\frac{7}{10b}$
C.$\frac{7}{10ab}$
D.$\frac{2a+3b}{10a^2b^2}$
答案
1.C
2. 化简$\frac{1}{x-1}+\frac{2}{1-x^2}$的结果为(
A.$x-1$
B.$\frac{3}{x^2 -1}$
C.$\frac{1}{x-1}$
D.$\frac{1}{x+1}$
D
)A.$x-1$
B.$\frac{3}{x^2 -1}$
C.$\frac{1}{x-1}$
D.$\frac{1}{x+1}$
答案
2.D
3. 计算$(x+y)÷\frac{x+y}{x}·\frac{x}{x+y}$的结果正确的是(
A.$x+y$
B.$\frac{x^2}{x+y}$
C.$\frac{1}{y}$
D.$\frac{1}{1+y}$
B
)A.$x+y$
B.$\frac{x^2}{x+y}$
C.$\frac{1}{y}$
D.$\frac{1}{1+y}$
答案
3.B
4.已知■÷$\frac{y-x}{2}$=$\frac{x}{x-y}$，则■表示的代数式是（
A.$-\frac{x}{2}$
B.$\frac{2x}{y^2 - x^2}$
C.$\frac{x}{2}$
D.$\frac{2x}{x^2 - y^2}$
A
）A.$-\frac{x}{2}$
B.$\frac{2x}{y^2 - x^2}$
C.$\frac{x}{2}$
D.$\frac{2x}{x^2 - y^2}$
答案
4.A
5. 下列计算不正确的是(
A.$\frac{xy}{x^2 - 2xy + y^2} ÷ \frac{xy^2 + x^2y}{x^2 - y^2} = \frac{1}{x - y}$
B.$( \frac{3x}{-2y} )^2 · ( \frac{2y}{-3x} )^3 = -\frac{2y}{3x}$
C.$\frac{x^2 + x}{x^2 + 2x + 1} · \frac{x^2 - 1}{x - 1} = x(x + 1)$
D.$\frac{y}{x^2} ÷ \frac{(-y)^2}{x^2} = \frac{1}{y}$
C
)A.$\frac{xy}{x^2 - 2xy + y^2} ÷ \frac{xy^2 + x^2y}{x^2 - y^2} = \frac{1}{x - y}$
B.$( \frac{3x}{-2y} )^2 · ( \frac{2y}{-3x} )^3 = -\frac{2y}{3x}$
C.$\frac{x^2 + x}{x^2 + 2x + 1} · \frac{x^2 - 1}{x - 1} = x(x + 1)$
D.$\frac{y}{x^2} ÷ \frac{(-y)^2}{x^2} = \frac{1}{y}$
答案
5.C
6. 计算$\frac{1}{a-1} · \frac{a^2 - 2a + 1}{a} ÷ \frac{1}{a}$的结果是
$a-1$
.答案
6.$a-1$
7. 计算$(1-\dfrac{1}{x+2})÷\dfrac{x+1}{x^2-4}$的结果为________。
答案
7.$x-2$
8. 已知$n$是正整数，比较大小：$\frac{2n-1}{2n}$
$＜$
$\frac{2n}{2n+1}$答案
8. $＜$ 解析 已知 $n$ 是正整数，则
$\frac{2n-1}{2n}-\frac{2n}{2n+1}=\frac{(2n-1)(2n+1)-2n· 2n}{2n(2n+1)}=\frac{4n^2-1-4n^2}{2n(2n+1)}=\frac{-1}{2n(2n+1)}＜0,\therefore \frac{2n-1}{2n}＜\frac{2n}{2n+1}.$
$\frac{2n-1}{2n}-\frac{2n}{2n+1}=\frac{(2n-1)(2n+1)-2n· 2n}{2n(2n+1)}=\frac{4n^2-1-4n^2}{2n(2n+1)}=\frac{-1}{2n(2n+1)}＜0,\therefore \frac{2n-1}{2n}＜\frac{2n}{2n+1}.$
