Question 116567
This particular problem that I'm working on says Divide: {{{(x^2+10x+24)/(x+4)}}}. For a problem like this, is the Distributive Property recommended?

<pre><font face = "book antiqua" size = 4><b>
No, the distributive property is recommended only when the denominator
contains ONLY ONE TERM.  But the denominator here is x+4 which contains
TWO terms.

If you were to use the distributive property you would have:

{{{(x^2+10x+24)/(x+4)}}}

{{{x^2/(x+4)+(10x)/(x+4)+24/(x+4)}}}

and none of those three fractions can be simplified.  So the
distributive law "complicates" rather than simplifies.

The correct way to simplify 

{{{(x^2+10x+24)/(x+4)}}}

is either by long division:
<font face = "courier new">
     <u>        x +  6</u>
x + 4)x² + 10x + 24
      <u>x² +  4x</u>
            6x + 24
            <u>6x + 24</u> 
                  0
</font>
getting quotient x + 6,

or by factoring the numerator

{{{(x^2+10x+24)/(x+4)}}}

as

{{{((x+4)(x+6))/(x+4)}}}

and then canceling the {{{(x+4)}}}'s,

{{{(cross(x+4)(x+6))/cross(x + 4)}}}

 leaving

{{{x+6}}}

Edwin</pre>