Question 378196
Use polynomial long division,

<pre>

          y^2 + 3
        _________________________________
y^2 - 3 | y^4 +  0y^3 +  0y^2 +  3y -  1
      -  (y^4 +  0y^3 -  3y^2)
       ----------------------------------
                         3y^2 +   3y -  1
                      - (3y^2 +   0y -  9)
                        ------------------
                                  3y +  8

</pre>
{{{(y^4+3y-1)/(y^2-3)=(y^2+3)+(3y+8)/(y^2-3)}}}