8.5E：练习
- Page ID
- 204828
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通过将复杂的有理表达式写成除法来简化它
在以下练习中，进行简化。
\(\frac{\frac{2a}{a+4}}{\frac{4a^2}{a^2−16}}\)
- 回答
-
\(\frac{a−4}{2a}\)
\(\frac{\frac{3b}{b−5}}{\frac{b^2}{b^2−25}}\)
\(\frac{\frac{5}{c^2+5c−14}}{\frac{10}{c+7}}\)
- 回答
-
\(\frac{1}{2(c−2)}\)
\(\frac{\frac{8}{d^2+9d+18}}{\frac{12}{d+6}}\)
\(\frac{\frac{1}{2}+\frac{5}{6}}{\frac{2}{3}+\frac{7}{9}}\)
- 回答
-
\(\frac{24}{26}\)
\(\frac{\frac{1}{2}+\frac{3}{4}}{\frac{3}{5}+\frac{7}{10}}\)
\(\frac{\frac{2}{3}−\frac{1}{9}}{\frac{3}{4}+\frac{5}{6}}\)
- 回答
-
\(\frac{20}{57}\)
\(\frac{\frac{1}{2}−\frac{1}{6}}{\frac{2}{3}+\frac{3}{4}}\)
\(\frac{\frac{n}{m}+\frac{1}{n}}{\frac{1}{n}−\frac{n}{m}}\)
- 回答
-
\(\frac{n^2+m}{m−n^2}\)
\(\frac{\frac{1}{p}+\frac{p}{q}}{\frac{q}{p}−\frac{1}{q}}\)
\(\frac{\frac{1}{r}+\frac{1}{t}}{\frac{1}{r^2}−\frac{1}{t^2}}\)
- 回答
-
\(\frac{rt}{t−r}\)
\(\frac{\frac{2}{v}+\frac{2}{w}}{\frac{1}{v^2}−\frac{1}{w^2}}\)
\(\frac{x−\frac{2x}{x+3}}{\frac{1}{x+3}+\frac{1}{x−3}}\)
- 回答
-
\(\frac{(x+1)(x−3)}{2}\)
\(\frac{y−\frac{2y}{y−4}}{\frac{2}{y−4}−\frac{2}{y+4}}\)
\(\frac{2−\frac{2}{a+3}}{\frac{1}{a+3}+\frac{a}{2}}\)
- 回答
-
\(\frac{4}{a+1}\)
\(\frac{4−\frac{4}{b−5}}{\frac{1}{b−5}+\frac{b}{4}}\)
在以下练习中，进行简化。
\(\frac{\frac{1}{3}+\frac{1}{8}}{\frac{1}{4}+\frac{1}{12}}\)
- 回答
-
\(\frac{1}{18}\)
\(\frac{\frac{1}{4}+\frac{1}{9}}{\frac{1}{6}+\frac{1}{12}}\)
\(\frac{\frac{5}{6}+\frac{2}{9}}{\frac{7}{18}−\frac{1}{3}}\)
- 回答
-
19
\(\frac{\frac{1}{6}+\frac{4}{15}}{\frac{3}{5}−\frac{1}{2}}\)
\(\frac{\frac{c}{d}+\frac{1}{d}}{\frac{1}{d}−\frac{d}{c}}\)
- 回答
-
\(\frac{c^2+c}{c−d^2}\)
\(\frac{\frac{1}{m}+\frac{m}{n}}{\frac{n}{m}−\frac{1}{n}}\)
\(\frac{\frac{1}{p}+\frac{1}{q}}{\frac{1}{p^2}−\frac{1}{q^2}}\)
- 回答
-
\(\frac{pq}{q−p}\)
\(\frac{\frac{2}{r}+\frac{2}{t}}{\frac{1}{r^2}−\frac{1}{t^2}}\)
\(\frac{\frac{2}{x+5}}{\frac{3}{x−5}+\frac{1}{x^2−25}}\)
- 回答
-
\(\frac{2x−10}{3x+16}\)
\(\frac{\frac{5}{y−4}}{\frac{3}{y+4}+\frac{2}{y^2−16}}\)
\(\frac{\frac{5}{z^2−64}+\frac{3}{z+8}}{\frac{1}{z+8}+\frac{2}{z−8}}\)
- 回答
-
\(\frac{3z−19}{3z+8}\)
\(\frac{\frac{3}{s+6}+\frac{5}{s−6}}{\frac{1}{s^2−36}+\frac{4}{s+6}}\)
\(\frac{\frac{4}{a^2−2a−15}}{\frac{1}{a−5}+\frac{2}{a+3}}\)
- 回答
-
\(\frac{4}{3a−2}\)
\(\frac{\frac{5}{b^2−6b−27}}{\frac{3}{b−9}+\frac{1}{b+3}}\)
\(\frac{\frac{5}{c+2}−\frac{3}{c+7}}{\frac{5c}{c^2+9c+14}}\)
- 回答
-
\(\frac{2c+29}{5c}\)
\(\frac{\frac{6}{d−4}−\frac{2}{d+7}}{\frac{2d}{d^2+3d−28}}\)
\(\frac{2+\frac{1}{p−3}}{\frac{5}{p−3}}\)
- 回答
-
\(\frac{(2p−5)}{5}\)
\(\frac{\frac{n}{n−2}}{3+\frac{5}{n−2}}\)
\(\frac{\frac{m}{m+5}}{4+\frac{1}{m−5}}\)
- 回答
-
\(\frac{m(m−5)}{4m^2+m−95}\)
\(\frac{7+\frac{2}{q−2}}{\frac{1}{q+2}}\)
在以下练习中，使用任一方法。
\(\frac{\frac{3}{4}−\frac{2}{7}}{\frac{1}{2}+\frac{5}{14}}\)
- 回答
-
\(\frac{13}{24}\)
\(\frac{\frac{v}{w}+\frac{1}{v}}{\frac{1}{v}−\frac{v}{w}}\)
\(\frac{\frac{2}{a+4}}{\frac{1}{a^2−16}}\)
- 回答
-
2 (a−4)
\(\frac{\frac{3}{b^2−3b−40}}{\frac{5}{b+5}−\frac{2}{b−8}}\)
\(\frac{\frac{3}{m}+\frac{3}{n}}{\frac{1}{m^2}−\frac{1}{n^2}}\)
- 回答
-
\(\frac{3mn}{n−m}\)
\(\frac{\frac{2}{r−9}}{\frac{1}{r+9}+\frac{3}{r^2−81}}\)
\(\frac{x−\frac{3x}{x+2}}{\frac{3}{x+2}+\frac{3}{x−2}}\)
- 回答
-
\(\frac{(x−1)(x−2)}{6}\)
\(\frac{\frac{y}{y+3}}{2+\frac{1}{y−3}}\)
日常数学
电子设备通过并联连接两个电阻器形成的电路的电阻为\(\frac{1}{\frac{1}{R1}+\frac{1}{R2}}\)
- 简化复杂分数\(\frac{1}{\frac{1}{R1}+\frac{1}{R2}}\)
- 找出 R1=8 和 R2=12 时电路的电阻
- 回答
-
- \(\frac{R1R2}{R2+R1}\)
- \(\frac{24}{5}\)
熨烫 Lenore 可以在小时内为她的家庭生意熨烫。 她的女儿需要 h+2 个小时才能完成熨烫。 如果 Lenore 和她的女儿一起工作，使用 2 个熨斗，那么他们完成所有熨烫所需的小时数是\(\frac{1}{\frac{1}{h}+\frac{1}{h+2}}\)
- 简化复杂分数\(\frac{1}{\frac{1}{h}+\frac{1}{h+2}}\)
- 找出如果 h=4，Lenore 和她的女儿一起工作需要多少小时才能完成熨烫
写作练习
在本节中，您学会了用\(\frac{\frac{3}{x+2}}{\frac{x}{x^2−4}}\)两种方法来简化复杂分数：
把它改写为分区问题
将分子和分母乘以 LCD
你更喜欢哪种方法？ 为什么？
- 回答
-
答案会有所不同。
Efraim 想\(\frac{\frac{1}{a}+\frac{1}{b}}{\frac{1}{a}−\frac{1}{b}}\)通过取消分子和分母中的变量来开始简化复分数。 解释 Efraim 的计划出了什么问题。
自检
ⓐ 完成练习后，使用这份清单来评估你对本节目标的掌握程度。
ⓑ 看完清单后，你认为你为下一节做好了充分的准备吗？ 为什么或者为什么不呢？