8.6E：练习
- Page ID
- 204794
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求解有理方程
在以下练习中，求解。
\(\frac{1}{a}+\frac{2}{5}=\frac{1}{2}\)
- 回答
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10
\(\frac{5}{6}+\frac{3}{b}=\frac{1}{3}\)
\(\frac{5}{2}−\frac{1}{c}=\frac{3}{4}\)
- 回答
-
\(\frac{4}{7}\)
\(\frac{6}{3}−\frac{2}{d}=\frac{4}{9}\)
\(\frac{4}{5}+\frac{1}{4}=\frac{2}{v}\)
- 回答
-
\(\frac{40}{21}\)
\(\frac{3}{7}+\frac{2}{3}=\frac{1}{w}\)
\(\frac{7}{9}+\frac{1}{x}=\frac{2}{3}\)
- 回答
-
−9
\(\frac{3}{8}+\frac{2}{y}=\frac{1}{4}\)
\(1−\frac{2}{m}=\frac{8}{m^2}\)
- 回答
-
−2、4
\(1+\frac{4}{n}=\frac{21}{n^2}\)
\(1+\frac{9}{p}=−\frac{20}{p^2}\)
- 回答
-
−5、−4
\(1−\frac{7}{q}=−\frac{6}{q^2}\)
\(\frac{1}{r+3}=\frac{4}{2r}\)
- 回答
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−6
\(\frac{3}{t−6}=\frac{1}{t}\)
\(\frac{5}{3v−2}=\frac{7}{4v}\)
- 回答
-
14
\(\frac{8}{2w+1}=\frac{3}{w}\)
\(\frac{3}{x+4}+\frac{7}{x−4}=\frac{8}{x^2−16}\)
- 回答
-
\(-\frac{4}{5}\)
\(\frac{5}{y−9}+\frac{1}{y+9}=\frac{18}{y^2−81}\)
\(\frac{8}{z−10}+\frac{7}{z+10}=\frac{5}{z^2−100}\)
- 回答
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−13
\(\frac{9}{a+11}+\frac{6}{a−11}=\frac{7}{a^2−121}\)
\(\frac{1}{q+4}−\frac{7}{q−2}=1\)
- 回答
-
没有解决办法
\(\frac{3}{r+10}−\frac{4}{r−4}=1\)
\(\frac{1}{t+7}−\frac{5}{t−5}=1\)
- 回答
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−5、−1
\(\frac{2}{s+7}−\frac{3}{s−3}=1\)
\(\frac{v−10}{v^2−5v+4}=\frac{3}{v−1}−\frac{6}{v−4}\)
- 回答
-
没有解决办法
\(\frac{w+8}{w^2−11w+28}=\frac{5}{w−7}+\frac{2}{w−4}\)
\(\frac{x−10}{x^2+8x+12}=\frac{3}{x+2}+\frac{4}{x+6}\)
- 回答
-
没有解决办法
\(\frac{y−3}{y^2−4y−5}=\frac{1}{y+1}+\frac{8}{y−5}\)
\(\frac{z}{16}+\frac{z+2}{4z}=\frac{1}{2z}\)
- 回答
-
−4
\(\frac{a}{9}+\frac{a+3}{3a}=\frac{1}{a}\)
\(\frac{b+3}{3b}+\frac{b}{24}=\frac{1}{b}\)
- 回答
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−8
\(\frac{c+3}{12c}+\frac{c}{36}=\frac{1}{4c}\)
\(\frac{d}{d+3}=\frac{18}{d^2−9}+4\)
- 回答
-
2
\(\frac{m}{m+5}=\frac{50}{m^2−25}+6\)
\(\frac{n}{n+2}=\frac{8}{n^2−4}+3\)
- 回答
-
1
\(\frac{p}{p+7}=\frac{98}{p^2−49}+8\)
\(\frac{q}{3q−9}−\frac{3}{4q+12}=\frac{7q^2+6q+63}{24q^2−216}\)
- 回答
-
没有解决办法
\(\frac{r}{3r−15}−\frac{1}{4r+20}=\frac{3r^2+17r+40}{12r^2−300}\)
\(\frac{s}{2s+6}−\frac{2}{5s+5}=\frac{5s^2−3s−7}{10s^2+40s+30}\)
- 回答
-
没有解决办法
\(\frac{t}{6t−12}−\frac{5}{2t+10}=\frac{t^2−23t+70}{12t^2+36t−120}\)
求解特定变量的有理方程
在以下练习中，求解。
\(\frac{C}{r}=2π\)对于 r
- 回答
-
\(r=\frac{C}{2π}\)
\(\frac{I}{r}=P\)对于 r
\(\frac{V}{h}=lw\)对于 h
- 回答
-
\(h=\frac{v}{lw}\)
\(\frac{2A}{b}=h\)对于 b
\(\frac{v+3}{w−1}=\frac{1}{2}\)对于 w
- 回答
-
w=2v+7
\(\frac{x+5}{2−y}=\frac{4}{3}\)对于 y
\(a=\frac{b+3}{c−2}\)对于 c
- 回答
-
\(c=\frac{b+3+2a}{a}\)
\(m=\frac{n}{2−n}\)对于 n
\(\frac{1}{p}+\frac{2}{q}=4\)对于 p
- 回答
-
\(p=\frac{q}{4q−2}\)
\(\frac{3}{s}+\frac{1}{t}=2\)对我们来说
\(\frac{2}{v}+\frac{1}{5}=\frac{1}{2}\)对于 w
- 回答
-
\(w=\frac{15v}{10+v}\)
\(\frac{6}{x}+\frac{2}{3}=\frac{1}{y}\)对于 y
\(\frac{m+3}{n−2}=\frac{4}{5}\)对于 n
- 回答
-
\(n=\frac{5m+23}{m}\)
\(\frac{E}{c}=m^2\)对于 c
\(\frac{3}{x}−\frac{5}{y}=\frac{1}{4}\)对于 y
- 回答
-
\(y=\frac{20x}{12−x}\)
\(\frac{R}{T}=W\)对于 T
\(r=\frac{s}{3−t}\)对于 t
- 回答
-
\(t=\frac{3r−s}{r}\)
\(c=\frac{2}{a}+\frac{b}{5}\)对于 a
日常数学
房屋绘画 Alain 可以在 4 天内粉刷房子。 Spiro 要花 7 天才能粉刷同一栋房子。 求解 t 的方程式\(\frac{1}{4}+\frac{1}{7}=\frac{1}{t}\)，得出如果他们一起工作需要多少天才能粉刷房子。
- 回答
-
\(2\frac{6}{11}\)天
Boating Ari 可以用潮流开船 18 英里，其时间与逆流行驶 10 英里所需的时间相同。 如果船的速度为 7 节，则求解 c 的方程\(\frac{18}{7+c}=\frac{10}{7−c}\)以得出电流的速度。
写作练习
为什么这个方程没有解\(\frac{3}{x−2}=\frac{5}{x−2}\)
- 回答
-
答案会有所不同。
Pete 认为这个方程\(\frac{y}{y+6}=\frac{72}{y^2−36}+4\)有两个解，y=−6 和 y=4。 解释为什么 Pete 错了。
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。
ⓑ 看完这份清单后，你会怎么做才能对所有目标充满信心？