From Förberedande kurs i matematik 1

The fraction consists of the numerator \displaystyle \frac{3}{x}-\frac{1}{x}, which we can directly simplify somewhat to give \displaystyle \frac{3}{x}-\frac{1}{x}=\frac{3-1}{x}=\frac{2}{x}, and the denominator \displaystyle \frac{1}{x-3}. If we are to rewrite the fraction as an expression with a single fraction sign, we need to augment the multiply the top and bottom of the whole fraction by \displaystyle x\left( x-3 \right) and then eliminate \displaystyle x and \displaystyle x-3:

\displaystyle \begin{align} & \frac{\frac{3}{x}-\frac{1}{x}}{\frac{1}{x-3}}=\frac{\frac{2}{x}}{\frac{1}{x-3}}=\frac{\frac{2}{x}}{\frac{1}{x-3}}\centerdot \frac{x\left( x-3 \right)}{x\left( x-3 \right)} \\ & \\ & =\frac{\frac{2}{x}\centerdot x\left( x-3 \right)}{\frac{1}{x-3}\centerdot x\left( x-3 \right)}=\frac{2\left( x-3 \right)}{x} \\ \end{align}