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

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

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

Use long division and partial fractions to simplify the rational function这句话什么意思