Question 1144668
<pre>
 {{{matrix(1,3,
(matrix(2,1,DIFFERENCE,QUOTIENT)),""="",(f(a+h)-f(a))/h )}}}

{{{f(x) = x/(x + 5)}}}
{{{f(a) = a/(a + 5)}}}
{{{f(a+h) = (a+h)/((a+h) + 5)=(a+h)/(a+h+5)}}}
{{{f(a+h)-f(a)=(a+h)/(a+h+5)-a/(a + 5)}}}
{{{f(a+h)-f(a)=((a+h)(a + 5)-a(a+h+5))/((a+5)(a+h+5))}}}
{{{f(a+h)-f(a)=(a^2+5a+ah + 5h-a^2-ah-5a)/((a+5)(a+h+5))}}}

Everything in the top cancels except terms that contain h,
and some of them may cancel.

{{{f(a+h)-f(a)=(5h)/((a+5)(a+h+5))}}}

Now we form the difference quotient by dividing by h on the
left, and doing the equivalent multiplication by 1/h on the
right. [Dividing by h and multiplying by 1/h are the same.]

{{{(f(a+h)-f(a))/h=expr(1/h)*((5h)/((a+5)(a+h+5)))}}}

The h's cancel on the right and we are left with

{{{matrix(1,3,
(matrix(2,1,DIFFERENCE,QUOTIENT)),""="",5/((a+5)(a+h+5)))}}}

Edwin</pre>