in this video we're going to talk about how to simplify rational expressions when adding or subtracting them whenever they have like denominators so let's start with this example 3x over 5 plus four x plus seven over five because these two fractions share the same denominator we can combine it as a single fraction so we can write it as three x plus four x plus seven all divided by the common denominator which is five three x plus four x is seven x and if we want to we can take out the gcf which is seven leaving behind x plus one so that's the final answer for this example let's try another one 7 over x minus 11 over x so we can combine it as a single fraction seven minus eleven over x and seven minus eleven is negative four so the answer is going to be negative four divided by x try this one seven x plus four divided by x plus two plus five x minus seven over x plus two so let's write it as a single fraction seven x plus five x i'm gonna put the like terms together plus four minus seven all divided by x plus two seven x plus five x is twelve x four minus seven is negative three so we can take out a three if we want so it's going to be four x minus one over x plus two and so that's it let's try one more example three x minus ten divided by x minus one minus five x minus twelve over x minus one now be careful with this one go ahead and try it so first let's write it as a single fraction so it's going to be three x minus ten now this negative sign applies to the 5x and negative 12. so initially i'm going to write it using parentheses before you combine like terms distribute the negative sign so it's going to be 3x minus 10 minus 5x plus 12. 3x minus 5x is negative 2x negative 10 plus 12 is positive 2. now let's take out the gcf which is negative two negative two x divided by negative two that's positive x and positive two divided by negative two is negative one so notice that we can cancel x minus one which means the final answer is simply minus two