We can add and subtract rational expressions in much the same way as we add and subtract numerical fractions. To add or subtract two numerical fractions with the same denominator, we simply add or subtract the numerators, and write the result over the common denominator.
To add or subtract two rational expressions with the same denominator, we simply add or subtract the numerators and write the result over the common denominator.
When the denominators are not the same, we must manipulate them so that they become the same. In other words, you must find a common denominator.