Loading http://wiki.math.se/jsMath/fonts/msam10/def.js
Solution 2.1:7a
From Förberedande kurs i matematik 1
If we multiply the top and bottom of the first fraction by
\displaystyle \begin{align}
& \frac{2}{x+3}-\frac{2}{x+5}=\frac{2}{x+3}\centerdot \frac{x+5}{x+5}-\frac{2}{x+5}\centerdot \frac{x+3}{x+3} \\
& =\frac{2\left( x+5 \right)-2\left( x+3 \right)}{\left( x+3 \right)\left( x+5 \right)}=\frac{2x+10-2x-6}{\left( x+3 \right)\left( x+5 \right)}=\frac{4}{\left( x+3 \right)\left( x+5 \right)} \\
\end{align}