Answer:
To find the common denominator, we need to multiply each fraction by the denominator of the other fraction. For example, for
[tex]2+\frac{1}{x}=\frac{2}{1}+\frac{1}{x}[/tex]
When need to multiply the first fraction by x and the second fraction by 1 as follows
[tex]\frac{2\cdot x}{1\cdot x}+\frac{1\cdot1}{x\cdot1}=\frac{2x}{x}+\frac{1}{x}[/tex]
Therefore, the numerator of the function is changed from 2 + 1/x to 2x/x + 1/x
In the same way, we can transform the denominator of the function as follows:
[tex]\frac{1}{x}-3=\frac{1}{x}-\frac{3}{1}=\frac{1\cdot1}{x\cdot1}-\frac{3\cdot x}{1\cdot x}=\frac{1}{x}-\frac{3x}{x}[/tex]
So, from step 2 to step 3, they change 2 + 1/x to 2x/x + 1/x and change 1/x -3 by 1/x - 3x/3. This is
[tex]\frac{2+\frac{1}{x}}{\frac{1}{x}-3}=\frac{\frac{2x}{x}+\frac{1}{x}}{\frac{1}{x}-\frac{3x}{x}}[/tex]
