Final answer:
The addition and subtraction of rational functions require a common denominator to combine the numerators directly, and common factors should be simplified after combining to get the simplest form of the result.
Step-by-step explanation:
When adding and subtracting rational functions, the common denominator is required. Rational functions have fractions with polynomials in the numerator and denominator, similar to simpler fractions. A common denominator ensures that each fraction is expressed in terms of the same divisor, allowing their numerators to be combined directly.
For example, to add 1/2 and 1/3, you would find a common denominator, which is 6. You would then convert each fraction accordingly: 1/2 becomes 3/6 and 1/3 becomes 2/6. After conversion, the numerators can be added: 3 + 2 to make 5/6, which is the sum.
Subtraction works similarly, where after finding the common denominator, you subtract the numerators to find the difference. If the fractions have common factors, simplifying them after addition or subtraction is a critical step to get the simplest form of the result.