When adding algebraic fractions…
- Find a Common Denominator: The first step is to find a common denominator. If you want to save yourself the work later on, you can identify the least common multiple of the denominators of the fractions now. This common denominator will allow you to add the fractions together.
- Rewrite the Fractions: Rewrite each fraction so that they all have the same denominator. To do this, multiply both the numerator and the denominator of each fraction by the necessary factor(s) to make the denominators the same. You can also write it as all one big fraction with the single denominator, but I prefer to keep them separate at this stage.
- Add the Numerators: Once the fractions have the same denominator, add their numerators together while keeping the common denominator unchanged. Remember to simplify the resulting expression by combining like terms.
- Simplify the Fraction (if possible): If the expression in the numerator can be simplified further by factoring or canceling out common factors, then do so.
- Check for Restrictions: When there are variables involved, you need to check if there are any restrictions on the variables that would make the expression undefined. If so, state the restrictions.
- Verify (Optional): To be absolutely sure, it can be good to verify by inputting a number into the original expression as well as the simplified one,
This all works similarly with subtraction, though when it comes to algebraic fraction, it’s always safest to turn subtraction expressions into addition with flipped positive/negative signs in the numerator.