Question 242699
<pre><font size = 4 color = "indigo"><b>
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?  

{{{(m^2-p^2)/(p-m)}}}

{{{((m-p)(m+p))/(p-m)}}}

Now you got that far. But you cannot cancel {{{m-p)}}} 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+m}}}.  Then you have

{{{((-p+m)(m+p))/(p-m)}}}

Now factor {{{-1}}} out of {{{-p+m}}}, like this {{{-1(p-m)}}}.
When you factor out -1 it changes both signs inside:

{{{(-1(p-m)(m+p))/(p-m)}}}

Now you can cancel the {{{(p-m)}}}'s

{{{(-1(cross(p-m))(m+p))/(cross(p-m))}}}

and you end up with

{{{-1(m+p)}}}

or

{{{-m-p}}}

Edwin</pre>