<PRE><B>Question 22394</B>
&lt;pre&gt;  14x - 7      x&lt;sup&gt;2&lt;/sup&gt; + 6x + 8      x&lt;sup&gt;2&lt;/sup&gt; + 2x
----------- · ------------- ÷ -----------
x&lt;sup&gt;2&lt;/sup&gt; + 3x - 4   2x&lt;sup&gt;2&lt;/sup&gt; + 5x - 3    x&lt;sup&gt;2&lt;/sup&gt; + 2x - 3

Invert the divided fraction and change the division to
multiplication:

  14x - 7      x&lt;sup&gt;2&lt;/sup&gt; + 6x + 8    x&lt;sup&gt;2&lt;/sup&gt; + 2x - 3
----------- · ------------- · -----------
x&lt;sup&gt;2&lt;/sup&gt; + 3x - 4   2x&lt;sup&gt;2&lt;/sup&gt; + 5x - 3      x&lt;sup&gt;2&lt;/sup&gt; + 2x

Factor all numerators and denominators:

   7(2x - 1)    (x + 4)(x + 2)    (x + 3)(x - 1)
------------- · --------------- · --------------
(x + 4)(x - 1)  (x + 3)(2x - 1)      x(x + 2)

Write the product of the numerators over the product of 
the denominators:

7(2x - 1)(x + 4)(x + 2)(x + 3)(x - 1)
-------------------------------------
(x + 4)(x - 1)(x + 3)(2x - 1)x(x + 2)

Cancel the (2x - 1)&#39;s

7&lt;s&gt;(2x - 1)&lt;/s&gt;(x + 4)(x + 2)(x + 3)(x - 1)
-------------------------------------
(x + 4)(x - 1)(x + 3)&lt;s&gt;(2x - 1)&lt;/s&gt;x(x + 2)

7(x + 4)(x + 2)(x + 3)(x - 1)
-----------------------------
(x + 4)(x - 1)(x + 3)x(x + 2)

Cancel the (x + 4)&#39;s

7&lt;s&gt;(x + 4)&lt;/s&gt;(x + 2)(x + 3)(x - 1)
-----------------------------
&lt;s&gt;(x + 4)&lt;/s&gt;(x - 1)(x + 3)x(x + 2)

7(x + 2)(x + 3)(x - 1)
----------------------
(x - 1)(x + 3)x(x + 2)

Cancel the (x + 2)&#39;s

7&lt;s&gt;(x + 2)&lt;/s&gt;(x + 3)(x - 1)
----------------------
(x - 1)(x + 3)x&lt;s&gt;(x + 2)&lt;/s&gt;

7(x + 3)(x - 1)
---------------
(x - 1)(x + 3)x

Cancel the (x - 1)&#39;s

7(x + 3)&lt;s&gt;(x - 1)&lt;/s&gt;
---------------
&lt;s&gt;(x - 1)&lt;/s&gt;(x + 3)x
 
7(x + 3)
--------
(x + 3)x

Cancel the (x + 3)&#39;s

7&lt;s&gt;(x + 3)&lt;/s&gt;
--------
&lt;s&gt;(x + 3)&lt;/s&gt;x

 7
---
 x

Edwin
AnlytcPhil@aol.com&lt;/pre&gt;</PRE>