Mistake 3 - Cancelling Parts of a Sum

Often times people will make the mistake of cancelling a part of a sum instead of a factor. So a lot of times when students look at this, it's a common error to say, "Oh, here's an x in my numerator and here's an x in my denominator and I can just cancel those out, and it equals 2." Be very careful of this! We don't cancel out parts of sums, but we do cancel out factors. So this would be the mistake, and here's why. Let's take the same thing, and let's put in some numbers for x (to see if they do actually equal 2 or not). It doesn't have to be a particular number. It can be any number. So let's say if x equaled 5. I if plug in a 5 then I have 5 plus 2 divided by 5, this is actually equal to seven-fifths. So notice that 5 plus 2 over 5 (if I were to cancel those out), that does not equal 2. So be really, really careful of this. The only way that we can cancel x's out – that are ones on the top and ones on the bottom (ones in the numerator and ones in the denominator) is actually if, say if you had this: if you had x plus 1 times x divided by x. Then since this is a factor and here's the denominator, then those can cancel out. So remember, you can cancel out factors, just not parts of a sum. So then you would have x plus 1 left over. So be really, really careful of cancelling these things out. Remember, this is a sum up here, not a product.