What i did was i factored out the numerator to be (m-p)(m+p) and then i canceled out the denominator with the numerator to equal m+p as my final answer and it was incorrect. Found 2 solutions by jsmallt9, Edwin McCravy:Answer by jsmallt9(3296) (Show Source):
The error was that (m-p) and (p-m) are not the same. You cannot cancel factors unless they are the same.
But you may recognize that (m-p) and (p-m) are negatives of each other. (Think about this and it will make sense.) So if we factor out a -1 from one of them then we will have matching factors to cancel:
Here is the correct way to handle what is called "reversed differences",
in this case and . You agree that and
are not the same quantity, right?
Now you got that far. But you cannot cancel and .
They are DIFFERENT quantities, just as and are
Here is the way to handle it. Write the second term first
and the first term second, that is, write as
. Then you have
Now factor out of , like this .
When you factor out -1 it changes both signs inside:
Now you can cancel the 's
and you end up with