X^2-4x+1/x-3 меньше 2

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вопрос

To solve the inequality x^2 - 4x + 1/(x - 3) < 2, we first need to rewrite it in a standard form:

x^2 - 4x + 1 < 2(x - 3)
x^2 - 4x + 1 < 2x - 6
x^2 - 6x + 7 < 0

Now we need to find the values of x that satisfy this inequality. To do that, we can factor the quadratic equation:

(x - 1)(x - 7) < 0

The solutions to this inequality are x < 1 and x > 7. Therefore, the values of x that satisfy x^2 - 4x + 1/(x - 3) < 2 are x < 1 and x > 7.