From Förberedande kurs i matematik 1

Because the numerators are \displaystyle a^{2}-ab=a\left( a-b \right) and \displaystyle a-b, both terms will have a common denominator \displaystyle a\left( a-b \right) if the top and bottom of the second term are multiplied by \displaystyle a:

\displaystyle \begin{align} & \frac{2a+b}{a^{2}-b}-\frac{2}{a-b}=\frac{2a+b}{a\left( a-b \right)}-\frac{2}{a-b}\centerdot \frac{a}{a} \\ & =\frac{2a+b-2a}{a\left( a-b \right)}=\frac{b}{a\left( a-b \right)} \\ \end{align}