Question 89233
<pre><b>
{{{(3/(x-5)+1)/(1-4/(x-5))}}}

Write the {{{1}}}'s as {{{1/1}}} so everything
will be fractions:

{{{(3/(x-5)+1/1)/(1/1-4/(x-5))}}}

Put parentheses around the top and bottom:

{{{((3/(x-5)+1/1))/((1/1-4/(x-5)))}}}

The LCD of all four denominators is {{{ x-5 }}}.
Put it over 1 and put parentheses around it, {{{ ((x-5)/1)}}}
Then multiply top and bottom by that:

{{{((x-5)/1)(3/(x-5)+1/1)/((x-5)/1)(1/1-4/(x-5))}}} 

Now use the distributive principle to remove the 
parentheses on the right:

{{{ (((x-5)/1)(3/(x-5))+((x-5)/1)(1/1))/(((x-5)/1)(1/1)-((x-5)/1)(4/(x-5)))}}}

Cancel the {{{x-5)}}}'s in the top left and the bottom right
terms and erase the {{{1}}}'s and we get

{{{(3 + (x-5))/((x-5)-4)}}}

Remove the parentheses and we get:

{{{(3+x-5)/(x-5-4)}}}

Combining terms on top and bottom, we end up with

{{{(x-2)/(x-9)}}}

Edwin</pre>