Question #3281

(x-14)(x+5)/(x-18)<0

Expert's answer

<img src="/cgi-bin/mimetex.cgi?%5Cfrac%7B%28x-14%29%28x+5%29%7D%7Bx-18%7D%20%3C%200,%20%5Chspace%7B6mm%7D%20x%20%5Cne%2018%20%5C%5C%20%28x-14%29%28x+5%29%20%3C%20x%20-%2018%20%5C%5C%20x%5E2%20-%209x%20-70%20%3C%20x%20-%2018%20%5C%5C%20x%5E2%20-%2010x%20-%2052%20%3C%200%20%5C%5C%20D%20=%2025%20+%2052%20=%2077%20%5C%5C%20x_1%20=%205%20+%20%5Csqrt%7B77%7D%20%5C%5C%20x_2%20=%205%20-%20%5Csqrt%7B77%7D%20%5C%5C%20x%20%5Cin%20%285%20-%20%5Csqrt%7B77%7D,%205%20+%20%5Csqrt%7B77%7D%29" title="\frac{(x-14)(x+5)}{x-18} < 0, \hspace{6mm} x \ne 18 \\ (x-14)(x+5) < x - 18 \\ x^2 - 9x -70 < x - 18 \\ x^2 - 10x - 52 < 0 \\ D = 25 + 52 = 77 \\ x_1 = 5 + \sqrt{77} \\ x_2 = 5 - \sqrt{77} \\ x \in (5 - \sqrt{77}, 5 + \sqrt{77})">

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