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[tex]\displaystyle \frac{x^{2} - x - 6 + (x + 3) \sqrt{ {x}^{2} - 4} }{ {x}^{2} + x - 6 + (x - 3) \sqrt{ {x}^{2} -4} } , x > 2[/tex]
[tex]\displaystyle \frac{x^{2} - x - 6 + (x + 3) \sqrt{ {x}^{2} - 4} }{ {x}^{2} + x - 6 + (x - 3) \sqrt{ {x}^{2} -4} } , x > 2[/tex]
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(x² - x - 6 + (x + 3)√(x² - 4))/(x² + x - 6 + (x - 3)√(x² - 4)) = ((x - 3)(x + 2) + (x + 3)√(x² - 4))/((x + 3)(x - 2) + (x - 3)√(x² - 4))
(x - 3)(x + 2) = x² - x - 6
(x + 3)(x - 2) = x² + x - 6
замена
x + 3 = a
x - 3 = b
x - 2 = m
x + 2 = n
(bn + a√mn) / (am + b√mn) = умножаем на сопряженное
(bn + a√mn)(am - b√mn) / ( am + b√mn)(am - b√mn) = (abmn - b²n√mn + a²m√mn - abmn) / (a²m² - b²mn) = (a²m√mn - b²n√mn)/(a²m² - b²mn) = √mn(a²m - b²n) / m(a²m - b²n) = √mn / m = √n/m
(x² - x - 6 + (x + 3)√(x² - 4))/(x² + x - 6 + (x - 3)√(x² - 4)) = √(x + 2)/(x - 2)