Rational Expressions: Addition and Subtraction

Adding and Subtracting Fractions Add the Numerators If you can, find the Least Common Denominator Find a Common Denominator Remember to Simplify if Possible! Simplify the following expressions: Subtract the Numerators

Add/Subtract Rational Expressions Same denominator! Half the work is done! CAREFUL with subtraction. Don’t forget to subtract each term. Combine Like Terms Make sure it can’t be simplified more State the values that x can not equal, then simplify: Excluded values of x: 5 and -3. These Make the ORIGINAL denominator equal 0. We assume that x can never be these values. Find when the denominator(s) is 0: Cancel

Add/Subtract Rational Expressions Simplify: In order to add the fractions, find a Common Denominator Since the denominators are equal, add the numerators (2x 2 )(x)=2x 3 is a common denominator, but if possible find a LEAST common denominator.

Add/Subtract Rational Expressions In order to subtract, find a common denominator Distribute numerators but leave the denominators factored Subtract since the denominators are equal, subtract. But be CAREFUL with subtraction. Make sure to distribute the negative if necessary. Combine like Terms Simplify: The easiest way to find a common denominator, is to multiply by the other given denominators.

Add/Subtract Rational Expressions If possible, factor to find a Smaller Common Denominator If possible, simplify before subtracting the fractions. Simplify, assuming x≠0,1/3: Since the denominators are equal, subtract the numerators Combine like Terms

Add/Subtract Rational Expressions Factor to make sure it is simplified. Simplify, assuming x≠-4,4: If possible, factor to find a Smaller Common Denominator The easiest way to find a common denominator, is to multiply by the factors of the other given denominators it is missing. Since the denominators are equal, add the numerators