Question 392657
Can you help me simplify (not "solve") {{{(x-3)/(x^3+x^2-10x-6)}}}

<pre>

The other tutor divided the wrong way.

x - 3 divided by x^3 + x^2 - 10x - 6

{{{(x-3)/(x^3+x^2-10x-6)}}}

Write it as {{{((x-3)/1)/((x^3+x^2-10x-6)/1)}}}



Multiply by {{{(1/(x-3))/(1/(x-3))}}}



{{{expr(((x-3)/1)/((x^3+x^2-10x-6)/1))*expr((1/(x-3))/(1/(x-3)))}}}

{{{expr((cross(x-3)/1)/((x^3+x^2-10x-6)/1))*expr((1/cross(x-3))/(1/(x-3)))}}}


{{{1/((x^3+x^2-10x-6)/(x-3))}}}

The denominator is {{{(x^3+x^2-10x-6)/(x-3))}}}

So we divide it out:

Either by long division or synthetic division:

     <u>       x² +  4x + 2</u>          3|1  1  -10  -6
x - 3)x³ +  x² - 10x - 6           |<u>   3   12   6</u> 
      <u>x³ - 3x²</u>                      1  4    2   0 
           4x² - 10x              x² + 4x² + 2  
           <u>4x² - 12x</u>
                  2x - 6
                  <u>2x - 6</u> 


Therefore

{{{1/((x^3+x^2-10x-6)/(x-3))}}}

becomes:

{{{1/(x^2+4x+2)}}}

Edwin</pre>