((x+1)(x+2)(x+3)/(x-1)(x-2)(x-3))<1

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вопрос

First, let's simplify the expression:

((x+1)(x+2)(x+3)/(x-1)(x-2)(x-3))

= [(x^2 + 3x + 2)(x+3)] / [(x^2 - 3x + 2)(x-3)]

= (x^3 + 3x^2 + 2x + 3x^2 + 9x + 6) / (x^3 - 3x^2 + 2x - 3x^2 + 9x - 6)

= (x^3 + 6x^2 + 11x + 6) / (x^3 + 6x^2 + 9x - 6)

Now, we need to find the values of x for which this expression is less than 1. We can simplify this further by canceling out common terms:

= (11x + 6) / (9x - 6)

Now, we want to find the values of x for which this expression is less than 1:

(11x + 6) / (9x - 6) < 1

11x + 6 < 9x - 6

11x - 9x < -6 - 6

2x < -12

x < -6

Therefore, the solution to the inequality ((x+1)(x+2)(x+3)/(x-1)(x-2)(x-3)) < 1 is x < -6.