Answer:
(x+3)/(x-4)
Step-by-step explanation:
[2x²/(x-4)(x-3)] - [x²+9/(x-4)(x-3)] =
(x²-9)/(x-4)(x-3) =
(x+3)(x-3)/(x-4)(x-3) =
x+3/x-4
2x²/x² - 7x + 12 - x² + 9/x² - 7x + 12
2x²/x² simplifies to just 2 (the x²s cancel out)
2 - 7x + 12 - x² + 9/x² - 7x + 12
add like terms: (2 + 12 + 12) + (-7x - 7x) - x² + 9/x²
= - x² - 14x + 9/x² + 26
