第四章:部分分式 Partial Fraction

第六章:角的形成及单位 Angles and Measurements

4.3 部分分式 Partial Fraction – 练习题
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}
(13) \frac{x^4+2x^3+x^2+2x}{x{(x^2+1)}^2} |
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}