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From Förberedande kurs i matematik 1

In the same way that we calculated fractions, we can subtract the terms' numerators if we first expand the fractions so that they have the same denominator. Because the denominators are x−x2=x(1−x) and x, the lowest common denominator is x(1−x),

1x−x2−x1=1x−x2−x11−x1−x=1x−x2−1−xx−x2=x−x21−(1−x)=x−x21−1+x=xx−x2.

This fraction can be simplified by eliminating the factor x from the numerator and denominator

xx−x2=xx(1−x)=11−x.