1. Adding and Subtracting Rational Expressions
Megan Thomas and Devon Tierney

2. Step 1
Just like adding and subtracting regular fractions, the first step is to find a common denominator. Two ways to go about doing this are to find the LCM of the two rational expressions or another method you could use is the factor method. It works by finding the prime factorization of each denominator, and then using a chart to find the factors needed for the common denominator.
Factor method.

3. Step 2
My common denominator will be 2x2. To convert the the 2x I need to multiply by 2x/2x, since the denominator already has one copy of x but needs a 2 and another x to be equal.

4. Step 3
Just like the 3/x2 I will have to multiply it by 2/2 and for the 1/2x, I will multiply by x/x to make all of these equal.

5. Step 4
Now that all three expressions have the same common denominator of 2x2, add the numerators together.

6. Step 5
After adding the three numerators together, the problem can still be further simplified by combing like terms. So combine the 4x and the 1x to give you 5x then just attach the positive 6 to the end to give you your final answer of: