The polynomial is subtracted using the distributive property.
.. (16k^3 -3v^4) -(-9k^3 +6v^4)
.. = 16k^3 -3v^4 +9k^3 -6v^4
.. = (16 +9)k^3 +(-3 -6)v^4
.. = 25k^3 -9v^4
"Invert" means different things in different contexts. Here we suppose it means you simply want the reciprocal of this difference:
.. (16k^3 -3v^4) -(-9k^3 +6v^4)
.. = 16k^3 -3v^4 +9k^3 -6v^4
.. = (16 +9)k^3 +(-3 -6)v^4
.. = 25k^3 -9v^4
"Invert" means different things in different contexts. Here we suppose it means you simply want the reciprocal of this difference: