Matematika

Pertanyaan

Tentukan batas batas nilai x yang memenuhi pertidaksamaan berikut x+1/x-2 < x-5/x-3

1 Jawaban

  • (x+1)/(x-2) < (x-5)/(x-3)
    (x+1)/(x-2) - (x-5)/(x-3) < 0
    {(x+1)(x-3) - (x-5)(x-2)} / (x-2)(x-3) < 0
    {x²-2x-3 - (x²-7x+10)} / (x-2)(x-3) < 0
    (5x - 13) / (x-2)(x-3) < 0
    - - - - - + + + + - - - - - - + + +
    --------•---------•---------•--------
    ````````` 2 `````` 13/5 `````` 3
    x < 2 atau 13/5 < x < 3

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