About Lesson
Decompose the following fractions into partial fractions
把下列分式分成部分分式
把下列分式分成部分分式
(1)
(2) ![Rendered by QuickLaTeX.com \frac{x+3}{x^2-3x+2}](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-b88acdcaac7836c06f4decccf7f01b89_l3.png)
![Rendered by QuickLaTeX.com \frac{x+3}{x^2-3x+2}](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-b88acdcaac7836c06f4decccf7f01b89_l3.png)
(3)
(4) ![Rendered by QuickLaTeX.com \frac{x^2+7}{(x+1){(x-1)}^2}](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-98e65849ad74e3edbae3a1f533d3c9ec_l3.png)
![Rendered by QuickLaTeX.com \frac{x^2+7}{(x+1){(x-1)}^2}](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-98e65849ad74e3edbae3a1f533d3c9ec_l3.png)
(5) ![Rendered by QuickLaTeX.com \frac{x+2}{(1+x^2)(1-x)}](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-3d45fb40ac2ddf3dbc512ade3790a152_l3.png)
![Rendered by QuickLaTeX.com \frac{x+2}{(1+x^2)(1-x)}](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-3d45fb40ac2ddf3dbc512ade3790a152_l3.png)
(6)
(7)
(8) ![Rendered by QuickLaTeX.com \frac{x}{x^3-1}](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-47c245c785d8cd8d471fe0e3d1ecd607_l3.png)
![Rendered by QuickLaTeX.com \frac{x}{x^3-1}](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-47c245c785d8cd8d471fe0e3d1ecd607_l3.png)
(9) ![Rendered by QuickLaTeX.com \frac{x^2}{x^2-3x+2}](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-26255fe19d0201580e76bbb20c98a903_l3.png)
![Rendered by QuickLaTeX.com \frac{x^2}{x^2-3x+2}](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-26255fe19d0201580e76bbb20c98a903_l3.png)
(10) ![Rendered by QuickLaTeX.com \frac{x^3-x-1}{(x-1)(x+2)}](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-4bd156228b69d6a4cf99cbdda34aaae3_l3.png)
![Rendered by QuickLaTeX.com \frac{x^3-x-1}{(x-1)(x+2)}](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-4bd156228b69d6a4cf99cbdda34aaae3_l3.png)
(11)
(12)
[bg_collapse view=”link” color=”#4a4949″ expand_text=”Hint” collapse_text=”Closed Hint” ]
[/bg_collapse]
![Rendered by QuickLaTeX.com \frac{x^3+1}{x^2{(2x-1)}^2}](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-c15272104f0f9fa65dea52a3895750a8_l3.png)
![Rendered by QuickLaTeX.com \frac{A}{x^2}+\frac{B}{x}+\frac{C}{{(2x-1)}^2}+\frac{D}{2x-1}](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-685543a7c63a9323e4159edec4a94337_l3.png)
(13)
| [bg_collapse view=”link” color=”#4a4949″ expand_text=”Hint” collapse_text=”Closed Hint” ]
, 令x= 0找A,用比较系数法找其他。[/bg_collapse]
![Rendered by QuickLaTeX.com \frac{x^4+2x^3+x^2+2x}{x{(x^2+1)}^2}](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-cd6a50a08708ae06d40737a2010491cb_l3.png)
![Rendered by QuickLaTeX.com \frac{A}{x}+\frac{Bx+C}{{(x^2+1)}^2}+\frac{Dx+E}{x^2+1}](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-af854200433671cd81fd8c8d9b60efb1_l3.png)
Answer 答案:
(1)
![Rendered by QuickLaTeX.com \frac{1}{x-2}-\frac{1}{x+5}](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-1457fb27e9457146639cca39db100daf_l3.png)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
(11)
(12)
(13)