2025年自我提升与评价八年级数学上册人教版第148页答案
1. 计算$\frac{a+1}{a}-\frac{1}{a}$的结果是(
A
)
A.1
B.a
C.$\frac{1}{a}$
D.$-\frac{1}{a}$

答案

A

解析

$\frac{a+1}{a}-\frac{1}{a}=\frac{(a+1)-1}{a}=\frac{a}{a}=1$
A
2. 计算$\frac{2a}{a+1}+\frac{2}{a+1}$的结果是(
A
)
A.2
B.$2a+2$
C.1
D.$\frac{4a}{a+1}$

答案

A

解析

$\frac{2a}{a+1}+\frac{2}{a+1}=\frac{2a+2}{a+1}=\frac{2(a+1)}{a+1}=2$，结果为2，选A。
3. 计算$\frac{a^{2}+b^{2}}{a-b}+\frac{2ab}{b-a}$的结果是(
A
)
A.$a-b$
B.$a+b$
C.$\frac{(a+b)^{2}}{a-b}$
D.$\frac{(a-b)^{2}}{a+b}$

答案

A

解析

$\begin{aligned}\frac{a^{2}+b^{2}}{a-b}+\frac{2ab}{b-a}&=\frac{a^{2}+b^{2}}{a-b}-\frac{2ab}{a-b}\\&=\frac{a^{2}+b^{2}-2ab}{a-b}\\&=\frac{(a - b)^{2}}{a - b}\\&=a - b\end{aligned}$
A
4. 计算$\frac{1}{x-1}-\frac{2}{x^{2}-1}$的结果是(
C
)
A.-1
B.$x-1$
C.$\frac{1}{x+1}$
D.$\frac{1}{x^{2}-1}$

答案

C

解析

$\begin{aligned}\frac{1}{x-1}-\frac{2}{x^{2}-1}&=\frac{1}{x-1}-\frac{2}{(x-1)(x+1)}\\&=\frac{x+1}{(x-1)(x+1)}-\frac{2}{(x-1)(x+1)}\\&=\frac{x+1 - 2}{(x-1)(x+1)}\\&=\frac{x - 1}{(x-1)(x+1)}\\&=\frac{1}{x+1}\end{aligned}$
C
5. 化简$\frac{a^{2}}{a-1}-(a+1)$的结果是(
A
)
A.$\frac{1}{a-1}$
B.$-\frac{1}{a-1}$
C.$\frac{2a-1}{a-1}$
D.$\frac{-2a-1}{a-1}$

答案

A

解析

$\begin{aligned}\frac{a^{2}}{a - 1} - (a + 1)&=\frac{a^{2}}{a - 1} - \frac{(a + 1)(a - 1)}{a - 1}\\&=\frac{a^{2} - (a^{2} - 1)}{a - 1}\\&=\frac{a^{2} - a^{2} + 1}{a - 1}\\&=\frac{1}{a - 1}\end{aligned}$
A