4.3 部分分式 Partial Fraction - 练习题 - 独中课程 | 线上补习 | 有效提升数学能力

Lesson: 4.3 部分分式 Partial Fraction – 练习题

About Lesson

Decompose the following fractions into partial fractions
把下列分式分成部分分式

(1) $\frac{7}{(x-2)(x+5)}$

(2) $\frac{x+3}{x^2-3x+2}$

(3) $\frac{3x-1}{{(x-3)}^2}$

(4) $\frac{x^2+7}{(x+1){(x-1)}^2}$

(5) $\frac{x+2}{(1+x^2)(1-x)}$

(6) $\frac{3-2x}{x^3+x^2+4x+4}$

(7) $\frac{11+7x}{4-3x^2-x^3}$

(8) $\frac{x}{x^3-1}$

(9) $\frac{x^2}{x^2-3x+2}$

(10) $\frac{x^3-x-1}{(x-1)(x+2)}$

(11) $\frac{3x^2-2x+3}{x^3-x^2+3x}$

(12) $\frac{x^3+1}{x^2{(2x-1)}^2}$

$\frac{A}{x^2}+\frac{B}{x}+\frac{C}{{(2x-1)}^2}+\frac{D}{2x-1}$

(13) $\frac{x^4+2x^3+x^2+2x}{x{(x^2+1)}^2}$ |

$\frac{A}{x}+\frac{Bx+C}{{(x^2+1)}^2}+\frac{Dx+E}{x^2+1}$ , 令x= 0找A，用比较系数法找其他。

Answer 答案：

(1) $\frac{1}{x-2}-\frac{1}{x+5}$

(2) $\frac{5}{x-2}-\frac{4}{x-1}$

(3) $\frac{8}{{(x-3)}^2}+\frac{3}{x-3}$

(4) $\frac{2}{x+1}+\frac{4}{{(x-1)}^2}-\frac{1}{x-1}$

(5) $\frac{3}{2(1-x)}+\frac{3x+1}{2(1+x^2)}$

(6) $\frac{1}{x+1}-\frac{1+x}{x^2+4}$

(7) $\frac{2}{1-x}+\frac{2}{x+2}-\frac{1}{{(x+2)}^2}$

(8) $\frac{1}{3(x-1)}-\frac{x-1}{3(x^2+x+1)}$

(9) $1+\frac{4}{x-2}-\frac{1}{x-1}$

(10) $x-1+\frac{1}{x-1}-\frac{1}{x+2}$

(11) $\frac{1}{x}+\frac{2x-1}{x^2-x+3}$

(12) $\frac{1}{x^2}+\frac{4}{x}+\frac{9}{2{(2x-1)}^2}-\frac{15}{2(2x-1)}$

(13) $\frac{1}{x}-\frac{x}{{(x^2+1)}^2}+\frac{2}{x^2+1}$

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