Question 626234
<pre>
{{{(((5w^2-27w+10)/(5w^2+23w-10))) / (((25w^2-20w+4)/(5w^2+23w-10)))}}} =

Write as the division of two fractions:

 {{{((5w^2-27w+10)/(5w^2+23w-10))}}}{{{"÷"}}}{{{((25w^2-20w+4)/(5w^2+23w-10))}}} = 

Invert the second fraction and change division to multiplication:

{{{((5w^2-27w+10)/(5w^2+23w-10))}}}{{{"×"}}}{{{((5w^2+23w-10)/(25w^2-20w+4))}}} = 

Factor all numerators and denominators:

{{{(((w-5)(5w-2))/((5w-2)(w+5)))}}}{{{"×"}}}{{{((5w-2)(w+5))/((5w-2)(5w-2)))}}} =

Cancel a pair of (5w-2)'s:

{{{(((w-5)(cross(5w-2)))/((cross(5w-2))(w+5)))}}}{{{"×"}}}{{{((5w-2)(w+5))/((5w-2)(5w-2)))}}} =

Cancel the (w+5)'s:

{{{(((w-5)(cross(5w-2)))/((cross(5w-2))(cross(w+5))))}}}{{{"×"}}}{{{((5w-2)(cross(w+5)))/((5w-2)(5w-2)))}}} =

Cancel another pair of (5w-2)'s:

{{{(((w-5)(cross(5w-2)))/((cross(5w-2))(cross(w+5))))}}}{{{"×"}}}{{{((cross(5w-2))(cross(w+5)))/((cross(5w-2))(5w-2)))}}} =

All that's left is:

{{{(w-5)/(5w-2)}}}

Edwin</pre>