Fractions represent a division. And the easiest way to solve this is to write is as a fraction and then reduce the fraction:
First we factor out the greatest common factor (GCF) in the numerator and denominator:
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.)
leaving:
which simplifies to:
P.S. Here is how it would look if we used long division:
-19s^(4)t^3 - 3s^3t^2 + 5s^(2)t + 19
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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