Question

12/(х^2-4)-7/(х^2-9)≤0

Answer 1

12/(х²-4) - 7/(х²-9) ≤0 <=>
<=> [12(x²-9) - 7(х²-4)] / (х²-4)(х²-9) ≤0 <=>
<=>  (12x²-108-7х²+28) / (х²-4)(х²-9) ≤0 <=>
<=> (5x²-80) / (х²-4)(х²-9) ≤0 <=>
<=> 5(x²-16) / (х²-4)(х²-9) ≤0 <=>
<=> 5(x-4)(x+4) / (х-2)(x+2)(х-3)(x+3) ≤0

x≠-2; x≠2; x≠-3; x≠3

___[-4]__-__(-3)___(-2)__-__(2)___(3)__-__[4]___

Ответ: [-4;-3) ∨ (-2;2) ∨ (3;4]