Question 152501
<pre><font size = 4 color="indigo"><b>
{{{4/(a-5)-1/(5-a)}}}

Notice that you have denominators
{{{a-5}}} and {{{5-a}}}. These are
called "reversed differences".

This is how we treat this: Take the
one which is not in descending order
{{{5-a}}}

write it in descending order:

{{{-a+5}}}

factor out {{{-1}}}, which changes
both signs:

{{{-1(a-5)}}}

or just {{{-(a-5)}}}

Now substitute that for{{{5-a}}}:

{{{4/(a-5)-1/(-(a-5))}}}

Cancel the negative sign on the
bottom of the second fraction with
the minus sign in front of the
second fraction,making it a plus
in front of the second fraction:

{{{4/(a-5)+1/(a-5)}}}

Now the denominators are the same,
so all we need do is combine the
two numerators over their common
denominator:

{{{(4+1)/(a-5)}}}

or

{{{5/(a-5)}}}

Edwin</pre>