Question 716108
Fractions represent a division. And the easiest way to solve this is to write is as a fraction and then reduce the fraction:
{{{(-57s^(6)t^(4)-9s^5t^(3)+15s^(4)t^(2)+57s^(2)t)/3s^(2)t}}}
First we factor out the greatest common factor (GCF) in the numerator and denominator:
{{{(3s^2t(-19s^4t^3-3s^3t^2+5s^2t+19))/(1*3s^2t)}}}
As we can see, we can reduce this fraction. (If we could not reduce the fraction then we would have to resort to long division.)
{{{(cross(3s^2t)(-19s^4t^3-3s^3t^2+5s^2t+19))/(1*cross(3s^2t))}}}
leaving:
{{{(-19s^4t^3-3s^3t^2+5s^2t+19)/1}}}
which simplifies to:
{{{-19s^4t^3-3s^3t^2+5s^2t+19}}}<br>
P.S. Here is how it would look if we used long division:
<pre>
         -19s^(4)t^3 - 3s^3t^2  + 5s^(2)t    + 19
         ______________________________________________  
3s^(2)t /-57s^(6)t^(4)-9s^5t^(3)+15s^(4)t^(2)+ 57s^(2)t
         -57s^(6)t^(4)
         ------------
                   0 - 9s^5t^(3)
                     - 9s^5t^3
                     ---------
                            0 + 15s^(4)t^(2)
                                15s^(4)t^(2)
                               -------------
                                          0 +57s^(2)t 
                                             57s^(2)t
                                             --------
                                                   0
</pre>