(8t³-9+15t-10t²)/(4t-3)
=(8t³-6t²-4t²+3t+12t-9)/(4t-3)
=[2t²(4t-3)-3t(4t-3)+3(4t-3)]/(4t-3)
=(4t-3)(2t²-3t+3)/(4t-3)
=2t²-3t+3
(8t³-9+15t-10t²)/(4t-3)
=(8t³-6t²-4t²+3t+12t-9)/(4t-3)
=[2t²(4t-3)-3t(4t-3)+3(4t-3)]/(4t-3)
=(4t-3)(2t²-3t+3)/(4t-3)
=2t²-3t+3