SOLUTION: Simplify this rational expression please!!!! {{{M^2-p^2}}}/p-m What i did was i factored out the numerator to be (m-p)(m+p) and then i canceled out the denominator with the

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Question 242699: Simplify this rational expression please!!!!
/p-m

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(3758)   (Show Source): You can put this solution on YOUR website!
You were very close. Factor the numerator:

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:

which simplifies to

or
Answer by Edwin McCravy(20064)   (Show Source): You can put this solution on YOUR website!

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
different quantities.

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



or



Edwin
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