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

Algebra ->  Polynomials-and-rational-expressions -> 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      Log On


   

Question 242699: Simplify this rational expression please!!!!
M%5E2-p%5E2/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) About Me  (Show Source):
You can put this solution on YOUR website!
You were very close. Factor the numerator:
%28%28m%2Bp%29%28m-p%29%29%2F%28p-m%29
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:
%28%28m%2Bp%29%28m-p%29%29%2F%28-1%29%28m-p%29
which simplifies to
%28m%2Bp%29%2F%28-1%29
or
-m-p

Answer by Edwin McCravy(20064) About Me  (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 m-p and p-m.  You agree that 5-2 and 2-5
are not the same quantity, right?  

%28m%5E2-p%5E2%29%2F%28p-m%29

%28%28m-p%29%28m%2Bp%29%29%2F%28p-m%29

Now you got that far. But you cannot cancel m-p%29 and p-m.
They are DIFFERENT quantities, just as 5-2 and 2-5 are
different quantities.

Here is the way to handle it.  Write the second term first
and the first term second, that is, write m-p as
-p%2Bm.  Then you have

%28%28-p%2Bm%29%28m%2Bp%29%29%2F%28p-m%29

Now factor -1 out of -p%2Bm, like this -1%28p-m%29.
When you factor out -1 it changes both signs inside:

%28-1%28p-m%29%28m%2Bp%29%29%2F%28p-m%29

Now you can cancel the %28p-m%29's

%28-1%28cross%28p-m%29%29%28m%2Bp%29%29%2F%28cross%28p-m%29%29

and you end up with

-1%28m%2Bp%29

or

-m-p

Edwin