Simplify 2x²/x²-7x+12 - x²+9/x²-7x+12

(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

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