Question 400287
Long division with polynomials is similar to long division with numbers.
<pre>
           2x^2
          ________________________________________
4x^3 - 1 / 8x^5 +  0x^4 +  0x^3 + (-6x^2) + 9x + 9
           8x^5 +                  -2x^2
          -------------------------------
                                   -4x^2  + 9x + 9
</pre>
Since 4x^3 will not divide into -4x^2 we must stop here. The -4x^2 + 9x + 9 is the remainder. And if you remember that you put remainders in a numerator with the divisor in the denominator, then you will see that:
{{{(8x^5-6x^2+9x+9)/(4x^3-1) =  2x^2 + (-4x^2+9x+9)/(4x^3-1)}}}