Question 660213
<pre>
{{{(f(x)-f(1))/(x-1)}}}

Let's start out working with the numerator f(x) - f(1)  only:

f(x) - f(1) = {{{1/x}}} - {{{1/1}}} = {{{1/x}}} - {{{1/1}}}·{{{x/x}}} = {{{1/x}}} - {{{x/x}}} = {{{(1-x)/x}}}

Now let's divide that by the denominator x - 1:

{{{(1-x)/x}}}÷{{{(x-1)}}} = {{{(1-x)/x}}}÷{{{(x-1)/1}}} = {{{(1-x)/x}}}·{{{1/(x-1)}}} 

Now we have to play a trick with the 

1 - x

First arrange it in descending order

-x + 1

Factor out -1

-1(x - 1)

Now replace the 1 - x by that in  {{{(1-x)/x}}}·{{{1/(x-1)}}} 

{{{(-1(x-1))/x}}}·{{{1/(x-1)}}}

Cancel the (x - 1)'s

{{{(-1(cross(x-1)))/x}}}·{{{1/(cross(x-1))}}}

{{{-1/x}}}

Edwin</pre>