Question 169314
<pre><font size = 4 color = "indigo"><b>
{{{matrix(1,3,(z^2 + 8z + 16)/(z^2 + 13z + 36), "÷", (z^2 + 4z)/(z^2 + 15z + 54))}}}

Invert the second fraction and change the division to
multiplication:

{{{matrix(1,3,(z^2 + 8z + 16)/(z^2 + 13z + 36), "×", (z^2 + 15z + 54)/(z^2 + 4z))}}}


Factor all four parts:

{{{matrix(1,3,((z+4)(z+4))/((z+9)(z+4)), "×", ((z+9)(z+6))/(z(z + 4)))}}}

Indicate the multiplication of numerators and denominators
making just one fraction:

{{{((z+4)(z+4)(z+9)(z+6))/((z+9)(z+4)z(z+4))}}}

Cancel the first {{{(z+4)}}} in the top with the first one in
the bottom:

{{{(cross((z+4))(z+4)(z+9)(z+6))/((z+9)cross((z+4))z(z+4))}}}

Cancel the other {{{(z+4)}}} in the top with the other one
in the bottom:

{{{(cross((z+4))cross((z+4))(z+9)(z+6))/((z+9)cross((z+4))z*cross((z+4)))}}}

Cancel the {{{(z+9)}}}'s

{{{(cross((z+4))cross((z+4))cross((z+9))(z+6))/(cross((z+9))cross((z+4))z*cross((z+4)))}}}

All that's left is

{{{(z+6)/z}}}

Edwin</pre>