Question 975014
<pre>
{{{(x-4)/(x^3-7x^2+2x+40)}}}

Divide numerator and denominator by the numerator x-4

Either long division or by synthetic division:

     <u>       x² -  3x - 10</u>
x - 4)x³ - 7x² +  2x + 40
      <u>x³ - 4x²</u>
          -3x² +  2x
          <u>-3x² + 12x</u>
                -10x + 40
                <u>-10x + 40</u>

or  

4 | 1 -7   2  40
  |<u>    4 -12 -40</u>
    1 -3 -10   0

either way the denominator factors as

{{{(x-4)/((x-4)(x^2-3x-10))}}}

Then as long as x is not 4, we can cancel (x-4)

{{{cross((x-4))/(cross((x-4))(x^2-3x-10))}}}

{{{1/(x^2-3x-10)}}}

You can leave it like that or factor the denominator:

{{{1/((x-5)(x+2))}}}

Edwin</pre>