Question 204652
<pre><font size = 4 color = "indigo"><b>
{{{(x^2+5x+4)/(x+3)^2}}}{{{"÷"}}}{{{(x+1)/(x^2-9)}}}

Invert the 2nd fraction and change {{{"÷"}}} to {{{"*"}}}

{{{(x^2+5x+4)/(x+3)^2}}}{{{"*"}}}{{{(x^2-9)/(x+1)}}}

Factor {{{x^2+5x+4}}} as {{{(x+4)(x+1)}}}

Factor {{{x^2-9}}} as {{{(x-3)(x+3)}}}

Write {{{(x+3)^2}}} as {{{(x+3)(x+3)}}}

Put parentheses around {{{x+1}}} as {{{(x+1)}}}

{{{((x+4)(x+1))/((x+3)(x+3))}}}{{{"*"}}}{{{((x-3)(x+3))/((x+1))}}}

Indicate the multiplication of the numerators and denominators
to write as a single fraction:


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

Cancel the {{{(x+1)}}}'s

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

Cancel the {{{(x+3)}}} in the top with one of the {{{(x+3)}}}'s
in the bottom:

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

and we are left with this:

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

You can leave it like that or you can "FOIL" out the top:

{{{(x^2+x-12)/(x+3)}}}

Edwin</pre>