Use long division and partial fractions to simplify the rational function

分类: 作业答案 • 2022-06-01 21:31:36

问题描述：

Use long division and partial fractions to simplify the rational function
(x^4+x^3−x^2−x+1) / (x^3−x)

答

分母：(x^3-x)=x(x^2-1) 分子：(x^4+x^3−x^2−x+1)=（x^4−x^2+x^3−x+1）=x^2(x^2-1)+x(x^2-1)+1 化简后：(x^4+x^3−x^2−x+1) / (x^3−x)=x+1+1/x(x^2-1)